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A fast contact detection algorithm for 3-D discrete element method

Erfan G.Nezami,Youssef M.A.Hashash *,Dawei Zhao,Jamshid Ghaboussi

2230Newmark Civil Engineering Laboratory,Department of Civil and Environmental Engineering,University of Illinois at

Urbana-Champaign,205North Mathews Avenue,Urbana,IL 61801,USA

Received 8December 2003;received in revised form 21July 2004;accepted 11August 2004

Abstract

In the discrete element method,determining the contact points between interacting particles and the associated contact normals at each time step is a critically important and time consuming https://www.wendangku.net/doc/51108817.html,mon-plane (CP)algorithm is one of the more e?ec-tive methods for contact detection when dealing with two-dimensional polygonal or three-dimensional polyhedral particles.A new approach,called fast common plane (FCP)method,is proposed to ?nd the common plane between polygonal particles.FCP approach recognizes that a common plane has identifying characteristics,which dramatically reduce the search space for the com-mon plane.In two-dimensions,the CP is found by checking only 5possible candidate planes.In three-dimensions,the candidate planes fall within 4types related to the geometry of the particles and their relative positions.Numerical experiments reveal that in three dimensions FCP algorithm can be up to 40times faster than available search methods for ?nding the common-plane.ó2004Elsevier Ltd.All rights reserved.

1.Introduction

The idea of using discrete particles in numerical simulations was introduced in the work of Born and Huang [1]and Maradudin [2],where atoms are de-scribed via the concentrated mass and contact force of interacting atoms.Eisenstadt [3]models bonds be-tween atoms by springs.Cundall [4]introduces the dis-crete element method (DEM)to simulate large deformations in jointed rock formations.Cundall and Strack [5]extend DEM to analyze assemblies of ideal-ized granular particles composed of circular disks and spheres.

During the past two decades,DEM has proved to be a reliable tool to study the behavior of granular materi-als in both micro-and macro-scale.DEM simulations have been used in large scale geophysical applications such as landslides [6,7]and ice ?ows [8],as well as many

industrial and mining applications including dragline excavation [9],mixing in tumblers,[10,11],and silo ?ll-ing [11].

At the micro-level,DEM is used to investigate distri-bution and evolution of micro parameters (such as con-tact normals and contact forces),and their relation to macro-parameters (such as stress and strain)[12,13].The numerical results are in good agreement with micro-mechanical observations from experimental tests on nat-ural sands [14,15],idealized photo-elastic sensitive rods [16,17],and spherical glasses [18].

The complexity of the behavior of granular materials and substantial computational time and e?ort required for DEM computations,however,had limited most of DEM simulations prior to 1990to assemblies of circular disks or spheres.Examples are the DEM codes BALL [19]and TRUBAL [20].Lin and NG [21]provide an extensive list of available circular or spherical DEM codes.In most soil-mechanics related applications,the assumption of spherical particles fails to capture essen-tial aspects of mechanical behavior of the particulate material.

Corresponding author.Tel.:+12173336986;fax:+12173339464.

E-mail address:hashash@https://www.wendangku.net/doc/51108817.html, (Y.M.A.Hashash).

https://www.wendangku.net/doc/51108817.html,/locate/compgeo

Computers and Geotechnics 31(2004)

575–587

As a result,during the last decade,many e?orts have been made to incorporate non-spherical particles in DEM implementation.This includes ellipses[22,23], connected circular segments[24],super-quadratics[25], polygons[26],ellipsoids[21],polyhedrons[26,27].

2.Contact detection schemes in DEM

Regardless of rapid advances in computer hardware and parallel computation techniques,the huge computa-tional time and e?ort required to calculate and update contact forces are still a major hindering factor in large scale DEM simulations.For complex particle geome-tries,such as three-dimensional polyhedrons,contact detection subroutines can easily take up to80%of the total analysis time.Applicability of a DEM code is di-rectly related to the e?ciency of the employed contact detection scheme.

Contact detection in DEM is usually performed in two independent stages.The?rst stage,referred to as neighbor search,is merely a rough search that aims to provide a list of all possible particles in contact.Among available algorithms for neighbor searching,the most re-cent ones include No Binary Search(NBS)contact detection algorithm[28]and DESS algorithm[29].A re-view of neighbor search methods is available in[30].

In the second stage,called geometric resolution,pairs of contacting particles obtained from the?rst stage are examined in more detail to?nd the contact points(or contact area if distributed contact forces are considered) and calculate the contact forces.Geometric resolution algorithms strongly depend on complexity of the geo-metric representation of particles.For example,if the boundaries of the particles are implicitly represented by a single function f(x,y,z)=0,then a closed form solu-tion is likely to be available(for example see[5]for contacts between disks and spheres[22],for two-dimen-sional ellipses,and[21]for three-dimensional ellipsoids). E?ciency of these contact detection schemes are mostly controlled by the simplicity of the resulting equations.

Where the boundary cannot be represented by a sin-gle function f(x,y,z)=0,such as in polygons or polyhe-drons,the contact detection can be quite cumbersome. Barbosa[26]introduces a simple algorithm for contact detection between polyhedrons that requires comparing all the vertices of one particle to all faces of the other one and vice versa.The algorithm has a high computa-tional complexity of order O(N2),with N being the num-ber of vertices.Williams and O?Connor[30]introduce Discrete Function Representation algorithm,DFR, which achieves a computational complexity of order O(N).In DFR,the contact between particles is calcu-lated by considering the interaction between the bound-ing boxes of particles.Krishnasamy and Jakiela[31]and later Feng and Owen[32]introduce energy-based meth-ods for?nding the contact forces,in which a potential energy function is de?ned for each contact as a function of the overlap area.Cundall[33]introduces the well-known class of‘‘Common-Plane’’(CP)methods:‘‘A common plane is a plane that,in some sense,bisects the space between the two contacting particles’’.If the two particles are in contact,then both will intersect the CP,and if they are not in contact,then neither inter-sects the CP.As a result of using CP,the expensive par-ticle-to-particle contact detection problem reduces to a much faster plane-to-particle contact detection problem. Once the CP is established between two particles,the normal to the CP de?nes the direction of the contact normal,which in turn de?nes the direction of the normal contact force between the two particles.This is espe-cially advantageous for vertex-to-vertex or edge-to-vertex contacts,where the de?nition of the contact normal is a non-trivial problem.The method has a com-plexity of order O(N)and has been successfully imple-mented in three-dimensional DEM code3DEC[27].

The following sections introduce a new approach to obtain the CP for polygonal(2-D)and polyhedral(3-D)particles.Determination of contact points and con-tact forces are not discussed.Particles are assumed to be convex,rigid or deformable,while concave particles can be modeled as a combination of several convex par-ticles attached to each other.

3.De?nition of the common plane

The CP is identi?ed by its unit vector normal,n[h1], and any point V0on it as shown in Fig.1.For any point V in the space,the‘‘distance’’d V of that point to any arbitrary plane in the space is de?ned as

d V?náeV0àVT;e1Twhereby,n is th

e unit vector normal to the plane and V0 is any point on that plane.Both V and V0are described

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in a global Cartesian coordinate system.Eq.(1)divides the space into positive and negative half-spaces,with points in positive half-space have positive distances and points in negative half-space have negative distances to the plane.For any polygonal or polyhedral particle A the‘‘distance’’d A of the particle to any plane in the space is de?ned as

d A?

maxed V

Tif d C

mined V

Tif d C

()

;e2T

where d V

A?h2 is the distance of a vertex V on the particle

to the plane(Eq.(1)),and min{?}and max{?}represent minimum and maximum values,respectively,taken

over all vertices of the particle.d C

A is the distance of

the centroid of the particle to the plane.If a face of the particle is parallel to the plane then more than ver-

tex can de?ne the distance d Aád C

A ?O?h3 is of no prac-

tical interest as the CP will never pass through centroid of a particle.Subscripts and superscripts in all equa-tions denote particles and vertices(points),respectively. The vertex(or each of the vertices)that de?ne the dis-tance in(2)is called the‘‘closest vertex’’of that particle to the plane.

For any two particles A and B,a CP is the plane which meets the following three conditions:

Condition1.

Centroids of particles A and B are located on opposite sides of the CP.In this paper it is assumed that the centroid of particle A is located on the negative side and that of particle B in the positive side of CP, Fig.2.

Condition2.

The gap,de?ned as d Bàd A,is a maximum. Condition3.

d A=àd B,

d A and d B ar

e the distances o

f particles A and B.

Condition1guarantees that the CP is between the particles.The gap d Bàd A is only a function of direction n of the CP and is independent of the location of the plane in space.Consequently,Condition2identi?es the direction n by maximizing the gap.Condition3spec-i?es the location of the CP by setting d A=àd B.For sep-arated particles the gap is always positive(d A<0and d B>0),while for particles in contact the gap is always negative(d A>0and d B<0).

Whenever d Bàd A>TOL,where TOL is a small pos-itive user-de?ned tolerance,then the particles are recog-nized as not in contact,no CP is developed.A‘‘potential contact’’is a contact for which0

4.Conventional algorithm for?nding the CP

Cundall[33]suggests a two-stage procedure for?nd-ing the CP:the?rst stage speci?es one point on the CP (referred to as the reference point,point M in Fig.3). The second stage is an iterative process,in which a nor-mal vector n,corresponding to the maximum gap,is found by rotating the CP around the reference point. In two-dimensions,the CP is a line and the rotation is performed around the reference point M.In three-dimensions,two arbitrary orthogonal axes are chosen in the CP with their origin at the reference point.The CP is then perturbed around each of them in both neg-ative and positive sense.If any perturbation produces a gap larger than that of the current CP,the new CP re-places the current one.In this case,the closest vertices and the reference point is updated based on the newly found CP[34].If all the perturbations produce smaller

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gaps than that of the current CP,the next iteration starts with a smaller perturbation.The iteration process starts from an initial guess(either the CP from the previous time step or the perpendicular bisector of the line that connects the centroids of the particles),and continues until the direction of the CP is found with reasonable accuracy.At any stage of iteration,if the gap exceeds a positive tolerance TOL then the iterative process halts and the contact is deleted.A gap larger than TOL indi-cates that the particles are too far from each other to make a contact.The total number of iterations depends on the accuracy of the initial guess of the CP.In general, the algorithm requires a large number of iteration steps. The number of iteration steps is especially high for the ?rst-time formation of the CP,where the initial guess and the actual CP are very di?erent.

5.Fast identi?cation of common plane candidates

When two particles are not in contact,the de?nition of the CP can be utilized to limit the number of candi-date common planes and thus signi?cantly reduce the computational cost of common plane selection.

5.1.CP identi?cation in2-D

Statement:In two-dimensions,the CP can be found by checking only5possible candidate planes.

The following provides a stepwise proof of the state-ment above leading to identi?cation of the5possible candidate planes.

Proof.Let A and B be the closest vertices for two not-in-contact particles A and B,respectively.

(i)The CP passes through the midpoint M of segment AB.

Let h measure the angle between the CP and the perpendicular bisector(PB)of the segment AB,as shown in Fig.4.Then

j d A j?j MA j cos h and j d B j?j MA j cos h?h4 : The Condition3(Section3)of CP de?nition, (d A=àd B),implies that j d A j=j d B j or

j MA j cos h?j MB j cos h)j MA j?j MB j:

[CP should pass through the midpoint M of segment AB.

(ii)CP is completely located within the space S

Space S is the area formed by rays Mm1,Mm2,Mm3 and Mm4,drawn from the midpoint M,parallel to edges AA1,BB1,AA2,and BB2,respectively(the shaded area in Fig.5)(A ray is the part of a straight line beginning at a given point and extending limitlessly in one direction).

Assume that line L,portion of which is located outside space S,is a candidate common plane(Fig.5). Then,vertex B1is closer to this line than vertex B.This implies that AB1and not AB are the closest vertices. This contradicts AB being the closest vertices and the geometric arrangement of the particles.Therefore,line L cannot be a candidate common plane.Similarly all lines located partially or completely outside space S cannot be candidate common planes.

[The common plane is completely located within space S.

(iii)The CP should produce the smallest angle with the PB of the line AB

From Fig.4,d Bàd A=j AB j?cos h

From Condition2,d Bàd A is maximum

)cos h is maximum

[angle h is minimum.

(iv)The CP is one of?ve candidate planes

The CP is the line that

is completely located in space S from proof(ii),and

578 E.G.Nezami et al./Computers and Geotechnics31(2004)575–587

makes the smallest possible angle with the PB of AB from proof (iii).If the PB of the segment AB,is completely located in space S (Fig.6(a)),then:

From proof (iii)the line that makes the smallest possible angle h with PB is the PB itself.The PB also satis?es proof (ii),

[The common plane is the PB (type a below).

If the PB is not located completely inside the space S (Fig.6(b)),then:

The PB is not the common plane.

The common plane is the line with the smallest possi-ble angle h to the PB (proof iii).[The common plane is one of the boundary rays Mm 1,Mm 2,Mm 3or Mm 4,(Mm 1in the ?gure,type b below).Any line inside space S other than on the boundaries will make a larger angle h .

Note that in Fig.6(a)candidate common planes superimposed to rays Mm 1and Mm 2will partly be outside space S and can be eliminated as candidate planes as per proof (ii).However,from an algorithmic/practical numerical implementation point of view it is easier to maintain these as candidate planes and eliminate them using check Conditions (1)&(3)as de?ned in Section 3

[the CP is one of the following candidates:

Type a :The perpendicular bisector of segment AB .Type b :The lines passing through the mid-point of segment AB and parallel to edges AA 1,AA 2of particle A ,or parallel to edges BB 1and BB 2of particle B .

The number of candidate planes is limited to ?ve.h

5.2.CP identi?cation in 3-D

Statement :In three-dimensions,the candidate planes fall within 4types related to the geometry of the parti-cles and their relative positions.

Proof.Let A and B be the closest vertices for two not-in-contact particles A and B ,respectively.

(i)The CP passes through the midpoint M of segment AB

Similar to the 2-D case,the CP should pass through the midpoint M .Note that in 3-D,PB and CP are both planes,rather than lines,and the angle h measures the dihedral angle between PB and CP (Fig.7).The dihedral angle is the angle made by two perpendiculars to the intersection line of two planes,one in each plane.

[The CP passes through the midpoint M of segment AB

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(ii)The CP completely located within the space S Rays Mm1and Mm2drawn parallel to edges AA1and

AA2

?h5 ,respectively,de?ne a semi-in?nite quarter-plane

m1Mm2,parallel to face A1AA2of particle A.(Fig.8(a)). In the same way,for every face of particle A that shares vertex A,and for every face of particle B that shares vertex B,a quarter-plane can be constructed,passing through the midpoint M,parallel to that face(Fig.8(b)). The space bounded between the quarter-planes associ-ated with particle A from one side,and those associated with particle B form the other side,de?nes the space S in 3-D.

Similar to2-D,any candidate common plane should be completely located inside the space S.Assume that plane P,portion of which is located outside space S,is a

candidate common plane(Fig.9).Then,vertex B1is closer to this plane than vertex B,which contradicts AB being the closest vertices.

[The CP completely located within the space S.

(iii)The CP should produce the smallest dihedral angle with the PB of segment AB

d Bàd A=j AB j?cos h still holds in3-D.From Con-dition2,

àd A is maximum when dihedral angle h is minimum.

(iv)The CP is one of four different types

The CP is the plane that

is completely located in space S from proof(ii),and makes the smallest possible dihedral angle with the PB plane of AB from proof(iii).

If the PB plane of segment AB,lies completely in space S,then:

From proof(iii)the plane that makes the smallest possible dihedral angle h with PB is the PB itself.The PB also satis?es proof(ii)

[The common plane is the PB(type a below).

If the PB plane is not completely located inside the space S,then:

The PB is not the common plane.

The common plane is the plane with the smallest pos-sible angle h to the PB(proof iii).

[The common plane contains at least one ray from the boundary.Any plane which is completely inside the space S and does not contain any of the boundary rays, makes a larger dihedral angle h with PB and cannot be a candidate common plane.The number of rays included in CP can be used to further categorize it:

The CP contains exactly two boundary rays.Then: If those two rays correspond to the same particle, then the CP contains the quarter-plane made by those rays.Therefore it is parallel to one of the faces of the particles(type b).

If those two rays correspond to di?erent particles, then the CP is parallel to corresponding edges from di?erent particles(type c).

The CP contains exactly one boundary ray.In this case,the CP is parallel to the corresponding particle edge(type d).

The CP contains more than two boundary rays.Then any two of them can be utilized to identify the CP (the result is either type b or type c.For example, for the speci?c geometry shown in Fig.10whereby face B1BB2is parallel to the edge AA1,the CP is par-allel to three edges BB1,BB2and AA1.So it can be

580 E.G.Nezami et al./Computers and Geotechnics31(2004)575–587

either identi?ed as type b (if BB 1and BB 2are chosen)or type c (if BB 1and AA 1,or BB 2and AA 1are cho-sen).In any case,the CP is the plane passing through the midpoint of AB ,parallel to the face B 1BB 2and edge AA 1.

[the only possible candidates for the CP are as follows:

Type a :The PB plane of segment AB .

Type b :The plane passing through the midpoint of segment AB parallel to one of the faces of particles A or B .For particle A ,only faces which include the vertex A are considered.For particle B ,only faces which include the vertex B are considered.

Type c :The plane passing through the midpoint of segment AB parallel to one edge from particle A and one edge from particle B .For particle A ,only those edges which share the vertex A are considered.For particle B ,only those edges which share the vertex B are considered.

Type d :The plane passing through the midpoint of segment AB parallel to one edge from one of the particles.The plane can be fully de?ned by using the Conditions of the common plane described in Section 3.Fig.11shows the CP containing only one ray (Mm 1),parallel to the edge BB 1of block B.Condition 2states

that d B àd A is a maximum,while Condition 3states that d A =àd B .By substituting Condition 3into Condi-tion 2:

)2d B is a maximum,)d B is a maximum.

For this condition to be satis?ed,the distance of particle B ,d B ,to CP is de?ned by a line segment BB 0perpendicular to ray Mm 1.By de?nition BB 0de?nes the normal to CP and therefore the CP is fully de?ned.This can be proved as follows:suppose that BB 0is not the normal to CP,and BH is normal to CP (d B =j BH j )BHB 0forms a right triangle whose hypote-nuse is BB 0and thus j BB 0j P j BH j .It is therefore possible to ?nd another plane passing through Mm 1with a larger distance d B =j BB 0j that maximizes d B .That is the common plane.

The normal to CP can be found as follows:

BB 0(unit vector n BB 0)is perpendicular to ray Mm 1and therefore,edge BB 1(unit vector n BB 1),Fig.11n BB 0?n BB 1:

e3a T

Let n AB be the unit vector along segment AB .As BB 0,AB and BB 1are in the same plane,BB 0is perpendicular to n BB 1 n AB n BB 0?en BB 1 n AB T;e3b Twhere is the vector product.From Eqs.(3a)and (3b)n BB 0?n BB 1 en BB 1 n AB T;

e4T

n BB 0,is normal to the CP;)n =n BB 0.

Hence,from Eq.(4),normal to the CP is given by n ??n BB 1 en BB 1 n AB T;

e5T

±is used to adjust the direction of the CP based on Con-dition 1.h

6.FCP algorithm

6.1.Particles not in contact

The FCP algorithm to ?nd the CP consists of the fol-lowing steps (Fig.12):

Step 1.Initial guess:if there is a CP from previous DEM time step then use it as the initial guess for the CP in this time step.Otherwise,set the CP as the PB plane of the line connecting the centroids of the two particles.

Step 2.For this CP,?nd closest vertices AB in parti-cles A and B .This can be performed by a quick search of the distances of all the vertices of particles to the CP,considering the sign convention for each particle.Among all segments such as AB that connect a closest vertex A of particle A to a closest vertex B of particle B ,the one with the shortest length is chosen.If

E.G.Nezami et al./Computers and Geotechnics 31(2004)575–587581

than one pair of closest vertices have the shortest length (i.e.,those vertices are equidistant),then any of them can be chosen to proceed with the algorithm.

Step3.For the two closest vertices A and B found in Step2,check all candidate planes of Section5and?nd the one with the largest gap.If any candidate plane pro-duces a gap larger than TOL,then halt the algorithm as the particles are too far from each other to make any, real or potential,contact.If the gap is less than zero then a real contact is detected and an additional step is re-quired as described in Section6.2.

Step4.If the CP obtained in Step3is the same as the

one in Step2,then it is the correct common plane.Oth-erwise go to Step2.

This is an iterative algorithm,with each iteration con-sisting of steps2–4.The number of iterations required to ?nd the CP,is usually very small and in most cases is less than2(see examples in Section7.2).This is mainly be-cause the iteration is done to locate the two closest ver-tices,rather than the CP itself.

6.2.Particles in contact

For particles in contact,Fig.13(a),an additional step is performed before the algorithm of Section6.1is used, to temporarily separate the particles.This is accom-plished by translating the two particles in a direction perpendicular to the CP from the previous time step (Fig.13(b)).The translation distance TRAN for each particle should be as small as possible in order to make sure that the separated con?guration of particles is not much di?erent from the original con?guration.How-ever,it should be large enough to ensure the particles are not in https://www.wendangku.net/doc/51108817.html,e of a value of TRAN equal to the gap calculated for those particles in the previous DEM time step is recommended.The CP is then deter-mined for this separated con?guration.The CP of parti-cles A and B in their original con?guration(Fig.13(c))is assumed to be the same as that of the separated con?guration.

6.3.Approximation of CP

In most DEM applications,the location of the CP is not required with a high degree of https://www.wendangku.net/doc/51108817.html,ually,an approximation would be su?cient.Errors introduced by assumptions such as overlapping of particles when in contact,rather than actual deformation in particle shapes,and simpli?ed constitutive models for contact force calculations are,in general,much larger than the error introduced by using an approximate CP. Although the relative position of two particles and con-sequently,the position of the CP,may change in every time step,the contact type as well as the two closest ver-tices to the CP,remain unchanged during a large num-ber of successive time steps.This suggests that an approximated CP in one time step can be obtained from the CP in the previous time step,by assuming that the contact type and the closest vertices remain unchanged. For contact type b,it is assumed that the CP remains parallel to the same face as the previous time step. For contact types c or d,it is assumed that the CP re-mains parallel to the same edges as the previous time step.

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For every particle,a variable PAD(particle accumu-lated displacement)keeps the accumulated displacement calculated based on the maximum vertex displacement at every time step

PAD ttD t?PAD ttj maxed uTje6Tin which d u is the displacement of any vertex of the par-ticle and function max(?)is the maximum value,taken over all particle vertices at time step t+D t.Whenever the value PAD associated with a particle becomes larger than0.5·TOL,a complete CP check(Sections5and6) is performed for all the particles in the vicinity of that particle,and the value PAD is set to zero for those par-ticles whose contacts are updated.As long as PAD for a particle is smaller than0.5·TOL the approximation method is employed.

FCP algorithm temporarily separates in-contact par-ticles based on the position of the CP from the previous time step.It is essential to make sure that a CP does exist in the previous time step.A potential contact should be detected before the?rst occurrence of a real contact.On the other hand,if the gap between two particles is larger than TOL then no CP is calculated for those particles. The choice of the threshold value,0.5·TOL,guaran-tees that complete contact detection will be performed when two particles have a relative displacement larger than or equal to TOL.This in turn warrants that a potential contact and a CP exist before the two particles get in contact.

7.Performance of the FCP algorithm

The performance of the FCP algorithm is demon-strated through a series of examples for particles in2-D and3-D.The computational time is compared with that using the conventional algorithm proposed in Cundall[33].

7.1.Contact detection in2-D

Fig.14depicts16pairs of static particles in various con?gurations in2-D.For each con?guration,the CP is calculated using both FCP algorithm and the

E.G.Nezami et al./Computers and Geotechnics31(2004)575–587583

conventional algorithm.The resulting CPs from both algorithms are identical.The speed up ratio R,de?ned as the ratio of the CPU run time for the conventional algorithm to that for FCP algorithm,is shown for each con?guration and varies from1to5.FCP is faster than conventional algorithm when R>

Fig.15.Particles with4vertices(tetrahedron),5vertices(pyramid),8vertices(cube)and14vertices implanted in

DBLOCK3D.

Fig.16.Speed up ratio of the CPU run time as function of number of particles:(a)accumulation of free falling particles in a box;(b)box side wall removal.

584 E.G.Nezami et al./Computers and Geotechnics31(2004)575–587

7.2.Contact detection in3-D

The FCP algorithm is implemented in a3-D DEM code DBLOKS3D developed by the authors.The program incorporates granular assemblies consisting of polyhedral particles with any combination of particle sizes and geometries.Several examples are simulated to illustrate features of the FCP algorithm. For all examples,particles are generated according to a user-de?ned grain size distribution criterion with a minimum size of2cm and a maximum size of4cm.

The speed up ratio R in3-D is computed for a series of examples with180,270,360,450and540particles. Each example consists of two separate stages.In the?rst stage the particles are dropped into a30·30cm box from a height of about30cm.In the second stage,the wall on the right hand side of the box is removed,allow-ing the particles to?ow.The particle geometries are cho-sen evenly from those shown in Fig.15.The speed up ratios for the?rst and the second stages of each example are then calculated from the contact detection algorithm CPU run time required for the?rst0.5s(20,000time steps)of the simulations.The results,for stage one and stage two,are plotted as a function of number of particles in Fig.16.The speed up ratio is dependent on the number of particles involved in the test as well as the nature of the test.The speed up ratio ranges from 12to38.

The relationship of particle geometry to CPU run time of the FCP algorithm is evaluated using assemblies of162,243,324and405particles for each of the geom-etries shown in Fig.15.The particles are dropped on the ground from a height of about30cm.The simulations are continued for1.25s(85,000time steps),until a stable con?guration is achieved.For all simulations that in-clude the same number of particles,the required CPU run time is normalized with respect to that of the corre-sponding simulation with4-vertex particles and is plot-ted in Fig.17.The required time for?nding the CP does not monotonically increase with number of particle vertices.In contrast,there is always a reduction in the CPU run time when the number of vertices increases from4to5.This suggests that for these examples,the complexity order of the FCP algorithm is smaller than O(N).The order of complexity is di?cult to determine as it is not only related to the geometry of particles but also to the portion of the total number of contacts which are detected through approximation algorithm of Section6.3,and the problem being simulated.

Fig.18shows an example with30,000particles accu-mulated into a80cm·80cm box,up to a height of about120cm(Fig.18(a)).Only the right and the back walls are shown in the?gure.Particle geometries are chosen evenly from those shown in Fig.15.The wall on the left and the front side of the box is then removed and the test is continued for1.5s(100,000time steps) until a stable con?guration is achieved for all particles.

E.G.Nezami et al./Computers and Geotechnics31(2004)575–587585

Fig.18(b)plots the view of the assembly at di?erent times after removal of the wall.While the particles on the left and front experience high velocities,the particles on the right and the back are almost motionless.This al-lows extensive use of both approximation algorithm of Section 6.3for the slow moving particle in lieu of the ex-act CP plain detection algorithm of Sections 6.1and 6.2used for the fast moving particle.The average number of iterations required to ?nd the common plane using the FCP algorithm (Section 6)is 1.54,with a maximum number of iterations of 4.In general a small number of iterations is involved in FCP algorithm.A speed up ratio R =31is computed.

8.Conclusions

An e?cient algorithm is developed to ?nd the com-mon plane between two-dimensional polygons and three-dimensional polyhedrons.The algorithm takes advantage of properties of the CP to limit the search space for the plane.A quick updating algorithm is also introduced to approximate the new CP from the one in the previous time step.The method is then

compared with the available common-plane detection algorithm.It is observed that the proposed methodol-ogy is about 12–40times faster than the conventional algorithm.Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant No.CMS-0113745and Caterpillar,Inc.Any opinions,?ndings,and conclusions or recommendations expressed in this material are those of the authors and do not necessarily re?ect the views of the National Science Foundation or Caterpillar,Inc.This support is greatly acknowledged.The authors thank Ibrahim Mohammad for preparing the visualization code VisDEMSD.References

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E.G.Nezami et al./Computers and Geotechnics31(2004)575–587587

ADAMS常见问题

ADAMS 使用常见问题 1、ADAMS中的单位的问题开始的时候需要为模型设置单位。在所有的预置单位系统中,时间单位就是秒,角度就是度。可设置: MMKS--设置长度为毫米,质量为千克,力为牛顿。 MKS—设置长度为米,质量为千克,力为牛顿。 CGS—设置长度为厘米,质量为克,力为达因。 IPS—设置长度为英寸,质量为斯勒格(slug),力为磅。 2、如何永久改变ADAMS的启动路径？在ADAMS启动后,每次更改路径很费时,我们习惯将自己的文件存在某一文件夹下;事实上,在Adams的快捷方式上右击鼠标,选属性,再在起始位置上输入您想要得路径就可以了。 3、关于ADAMS的坐标系的问题。当第一次启动ADAMs/View时,在窗口的左下角显示了一个三视坐标轴。该坐标轴为模型数据库的全局坐标系。缺省情况下,ADAMS/View用笛卡儿坐标系作为全局坐标系。ADAMS/View将全局坐标系固定在地面上。当创建零件时,ADAMS/View给每个零件分配一个坐标系,也就就是局部坐标系。零件的局部坐标系随着零件一起移动。局部坐标系可以方便地定义物体的位置,ADAMS/View也可返回如零件的位置——零件局部坐标系相对于全局坐标系的位移的仿真结果。局部坐标系使得对物体上的几何体与点的描述比较方便。物体坐标系不太容易理解。您可以自己建一个ｐａｒｔ,通过移动它的位置来体会。 4、关于物体的位置与方向的修改可以有两种途径修改物体的位置与方向,一种就是修改物体的局部坐标系的位置,也就就是通过ＭＯＤＩＦＹ物体的ｐｏｓｉｔｉｏｎ属性;令一种方法就就是修改物体在局部坐标系中的位置,可以通过修改控制物体的关键点来实现。我感觉这两种方法的结果就是不同的,但就是对于仿真过程来说,物体的位置就就是质心的位置,所以对于仿真就是一样的。 5、关于ADAMS中方向的描述。对于初学的人来说,方向的描述不太容易理解。之前我们都就是用方向余弦之类的量来描述方向的。在ADAMS中,为了求解方程就是计算的方便,使用欧拉角来描述方向。就就是用绕坐标轴转过的角度来定义。旋转的旋转轴可以自己定义,默认使用313,也就就是先绕ｚ轴,再绕ｘ轴,再绕ｚ轴。 6、Marker点与Pointer点区别 Marker:具有方向性, 大部分情況都就是伴随物件自动产生的,而 Point不具有方向性, 都就是用户自己建立的;Marker点可以用来定义构件的几何形状与方向,定义约束与运动的方向等,而Point点常用来作为参数化的参考点,若构件与参考点相连,当修改参考点的位置时,其所关联的物体也会一起移动或改变。

adams常用函数

1.step可能是最常用的: step(time,0,0,1,50)+ step(time,4,0,6,-100)+ step(tme,9,0,10,50) 函数原形STEP(A,x1,h1,x2,h2) 解释：由数组A的x值，生成区间（x1，h1）至（x2，h2）之间的阶梯曲线，返回y值的数据。举个常用的例子。比如STEP(time,1,0,2,100) time在adams中是个递增的变量，相当于一个数组。那么step的返回值就是随着time变化的值。这个例子将表示在time从（1，2）的过程中，返回值将从0，100。看看例子，两个小球，一个使用step 函数设置了位移，另外一个是参考。当然，这个变化过程，adams使用了缓和的图形，从其位移图中可以看出来。step既然是个返回值，就可以使用加减法了。如上例，如果设置下面的小球的位移如下：STEP(time,1,0,2,100)+step(time,2,0,3,400)+step(time,3,0,4,-200) 2.以前用过碰撞函数，有单向和双向函数的区分，其中系统的球面等碰撞为其特例！ IMPACT (Displacement Variable, Velocity Variable, Trigger for Displacement Variable, Stiffness Coefficient, Stiffness Force Exponent, Damping Coefficient, Damping Ramp-up Distance) BISTOP (Displacement Variable, Velocity Variable, Low Trigger for Displacement Variable, High Trigger for Displacement Variable, Stiffness Coefficient, Stiffness Force Exponent, Damping Coefficient, Damping Ramp-up Distance) 3.if函数这个函数最好不要使用，他的使用会带来突变，会使运算的时候不收敛。不过应急的时候还是可以一用。 if(time-1:1,0,if(time-2:0,-1,-1)) IF(Expression1: Expression2, Expression3, Expression4) adams要计算Expression1的值：如果他的值小于0，则执行Expression2语句，如果Expression1的值等于0，则执行Expression3语句，如果Expression1的值大于0，则执行Expression4语句我得if语句的意思是：如果时间小于1的时候，加速度为1，如果时间为1，加速度为0，如果时间大于1小于2，则加速度为0，如果时间大于、等于2则，加速度为-1 4. 我得一个想法就是利用sign函数构造比较常用的是给机构加上一个与运动方向相反的作用力等等可以先测量施加力对象的运动速度，然后利用速度的变化，插入measure到sign函数里面就可以获得与运动方向相反的作用力

ADAMS-STEP函数

在定义接触力时Normal Force有两个选项： 1、Restitution（Define a restitution-based contact）； 2、Impact（Define an impact contact）第二个选项就是利用IMPACT函数，它能方便地表达那种间歇碰撞力（即达到某一位移值才激发的碰撞力）。它的参数意义及力学基础： One-sided Impact (IMPACT) 1、理解：用只抗压缩的非线性的弹簧阻尼方法近似计算出单边碰撞力。 2、格式：IMPACT (Displacement Variable, Velocity Variable, Trigger for Displacement Variable, Stiffness Coefficient, Stiffness Force Exponent, Damping Coefficient, Damping Ramp-up Distance) 3、参数说明： Displacement Variable 实时位移变量值，通过DX、DY、DZ、DM等函数实时测量。 Velocity Variable 实时速度变量值，通过VX、VY、VZ、VM等函数实时测量。 Trigger for Displacement Variable 激发碰撞力的位移测量值。 Stiffness Coefficient or K 刚度系统。 Stiffness Force Exponent 非线性弹簧力指数。 Damping Coefficient or C 阻尼系数。

Damping Ramp-up Distance 当碰撞力被激发阻尼逐渐增大的位移值。 4、Impact函数的力学基理： IMPACT函数值由自变量值决定其有无： IMPACT = Off if s > so On if s <=so IMPACT函数的数学计算公式为: MAX {0, K(so - s)**e - Cv *STEP (s, so- d, 1, so ,0)} 参数说明： s ——位移变量 v ——速度变量 so——碰撞力的激发位移值 K ——刚度系数 C ——阻尼系数 D——阻尼逐渐增大的位移值

ADAMS中的函数

ADAMS/View中系统提供的数学函数大致分类介绍如下。（1）基本数学函数 ABS(x) 数字表达式x的绝对值 DIM(x1，x2) x1>x2时x1与x2之间的差值，x1<x2时返回0 EXP(x) 数字表达式x的指数值 LOG(x) 数字表达式x的自然对数值 LOG10(x) 数字表达式x的以10为底的对数值 MAG(x，y，z) 向量[x，y，z]求模 MOD(x1，x2) 数字表达式x1对另一个数字表达式x2取余数 RAND(x) 返回0到1之间的随机数 SIGN(x1，x2) 符号函数，当x2>0时返回ABS(x)，当x2<0时返回－ABS(x) SQRT(x) 数字表达式x的平方根值（2）三角函数 SIN(x) 数字表达式x的正弦值 SINH(x) 数字表达式x的双曲正弦值 COS(x) 数字表达式x的余弦值 COSH(x) 数字表达式x的双曲余弦值 TAN(x) 数字表达式x的正切值 TANH(x) 数字表达式x的双曲正切值 ASIN(x) 数字表达式x的反正弦值 ACOS(x) 数字表达式x的反余弦值 ATAN(x) 数字表达式x的反正切值 ATAN2(x1，x2) 两个数字表达式x1，x2的四象限反正切值

（3）取整函数 INT(x) 数字表达式x取整 AINT(x) 数字表达式x向绝对值小的方向取整 ANINT(x) 数字表达式x向绝对值大的方向取整 CEIL(x) 数字表达式x向正无穷的方向取整 FLOOR(x) 数字表达式x向负无穷的方向取整 NINT(x) 最接近数字表达式x的整数值 RTOI(x) 返回数字表达式x的整数部分位置/方向函数位置/方向函数用于根据不同输入变量计算有关位置或方向的参数。ADAMS/View中系统提供的位置/方向函数分类介绍如下。（1）位置函数 LOC_ALONG_LINE 返回两点连线上与第一点距离为指定值的点 LOC_CYLINDRICAL 将圆柱坐标系下坐标值转化为笛卡儿坐标系下坐标值 LOC_FRAME_MIRROR 返回指定点关于指定坐标系下平面的对称点 LOC_GLOBAL 返回参考坐标系下的点在全局坐标系下的坐标值 LOC_INLINE 将一个参考坐标系下的坐标值转化为另一参考坐标系下的坐标值并归一化 LOC_LOC 将一个参考坐标系下的坐标值转化为另一参考坐标系下的坐标值

ADAMS部分常用函数的说明

ADAMS常用函数的说明一、几个常用函数的说明 1、 STEP函数格式：STEP (x, x0, h0, x1, h1) 参数说明： x ―自变量，可以是时间或时间的任一函数 x0 ―自变量的STEP函数开始值，可以是常数或函数表达式或设计变量； x1 ―自变量的STEP函数结束值，可以是常数、函数表达式或设计变量； h0 ― STEP函数的初始值，可以是常数、设计变量或其它函数表达式； h1 ― STEP函数的最终值，可以是常数、设计变量或其它函数表达式。 2、 IF函数格式：IF(表达式1: 表达式2, 表达式3, 表达式4) 参数说明：表达式1－ADAMS的评估表达式；表达式2－如果的Expression1值小于0，IF函数返回的Expression2值；表达式3－如果表达式1的值等于0，IF函数返回表达式3的值；表达式4－如果表达式1的值大于0，IF函数返回表达式4的值；

例如：函数IF(time-2.5:0,0.5,1) 结果：0.0 if time < 2.5 0.5 if time = 2.5 1.0 if time > 2.5 3、AKISPL函数格式：AKISPL (First Independent Variable, Second Independent Variable，Spline Name, Derivati ve Order) 参数说明： First Independent Variable ——spline中的第一个自变量 Second Independent Variable(可选) ——spline中的第二自变量 Spline Name ——数据单元spline的名称 Derivative Order(可选) ——插值点的微分阶数，一般用0就可以了例如： function = AKISPL(DX(marker_1, marker_2), 0, spline_1) spline_1用下表中的离散数据定义：

adams常见函数总结

ADAMS常用函数总结在使用adams的过程中，由于函数比较多，大概有11种之多，如1、Displacement Fu nction 2、Velocity Functions 3、Acceleration Functions 4、Contact Functions 5、Spline Functions 6、Force in Object Functions 7、Resultant Force Functi ons 8、Math Functions 9、Data Element Access 10、User-Written Subroutine Invocation 11、Constants & Variables。在adams中也有帮助文档，但是对于初学者来说还是有一定的难度的，基于这种情况我总结了一下几种常用的函数，希望能够起到抛砖引玉的作用！ 1、STEP函数格式：STEP (x, x0, h0, x1, h1) 参数说明： x―自变量，可以是时间或时间的任一函数 x0 ―自变量的STEP函数开始值，可以是常数或函数表达式或设计变量； x1 ―自变量的STEP函数结束值，可以是常数、函数表达式或设计变量 h0 ―STEP函数的初始值，可以是常数、设计变量或其它函数表达式 h1 ―STEP函数的最终值，可以是常数、设计变量或其它函数表达式 2、IF函数格式：IF(表达式1: 表达式2, 表达式3, 表达式4) 参数说明：表达式1－ADAMS的评估表达式；表达式2－如果的Expression1值小于0，IF函数返回的Expression2值；表达式3－如果表达式1的值等于0，IF函数返回表达式3的值；表达式4－如果表达式1的值大于0，IF函数返回表达式4的值；例如：函数IF(time-2.5:0,0.5,1) 结果：0.0 if time < 2.5 0.5 if time = 2.5 1.0 if time > 2.5 3、AKISPL函数格式：AKISPL (First Independent Variable, Second Independent Variable，Spline Name, Derivative Order) 参数说明： First Independent Variable——spline中的第一个自变量 Second Independent Variable (可选) ——spline中的第二自变量Spline Name——数据单元spline的名称 Derivative Order (可选) ——插值点的微分阶数，一般用0就可以function = AKISPL(DX(marker_1, marker_2, marker_2), 0, spline_1) spline_1用下表中的离散数据定义自变量x 函数值y -4.0 -3.6 -3.0 -2.5 -2.0 -1.2

实测地质剖面测量工作小结

实测地质剖面测量工作小结二一一一年八月

一、剖面测量工作概况为了解红花园金矿扎村金矿外围金矿化带内的地层分布、构造格架、滑坡体出露范围及金矿化带特征，建立1:5000地质填图地层单元；指导找矿方向和工程布置，我项目部充分收集扎村金矿带资料，并结合前人的地质成果，综合研究,建立了本区构造格架及地层单元。在此基础上，项目部克服了本区覆盖很广泛的困难，甄选了实测剖面的位置。2011年5月16—17日在红花园金矿扎村金矿外围金矿化带南部施测了C—C′地质剖面，该剖面的施测目的为：详细划分地层单元，确定地层时代、组段，建立1:5000地质填图地层单元。2011年5月19—20日在金矿化带中部施测了B—B′地质剖面, 该剖面的施测目的为：确定滑坡体的出露宽度，认识金矿化带南矿段金矿化带特征及其周边岩性组段，为1:5000填图详细圈定滑坡体、界定金矿化带南矿段金矿化带及划分地层组段提供依据。2011年6月20日在金矿化带北部施测了A—A′地质剖面, 该剖面的施测目的为：了解金矿化带北矿段岩性，确定地层时代、组段，认识金矿化带北矿段金矿化带特征，为金矿化带北矿段1:5000填图提供依据。 A—A′剖面: 起点坐标X:2795385,Y:33614095,H:2216m； B—B′剖面：起点坐标X:2792235,Y:33613443,H:1722m； C—C′剖面：起点坐标X:2791016,Y:33612508,H:1679m；因测区被“扎村金矿”分割为北矿段和南矿段，区内构造较复杂，地层产状变化较大，北部和南部地层出露有一定差异，因此在北矿段和南矿段选择地层相对较发育出露较齐全，基岩露头较好的地段在北矿段实测1条，在南矿段实测2条共3条地质剖面。工作方法是由地质人员采用测绳、罗盘、GPS半仪器法进行地质剖面的地形线测制，然后分导线进行地质观察，描述，标本采集工作，最后进行资料整理采用展开法完成实测地质剖面图的绘制。参加测制工作人员有:测手杨翔宇、邓平，记录孙晓轩，计算王旭鹏，制图杨显旭。测制工作完成工作量如下:测制剖面长度4.06KM；采集标本13件。二、地质成果一）区域地质巍山县红花园金矿勘查区位于西南三江褶皱系兰坪----思茅中新生代坳陷北段之兰坪---巍山坳陷盆地内, 兰坪中新生代陆相盆地位于西南三江地区南段，在晚古生代晚期，由金沙江洋向西俯冲与澜沧江洋的向东俯冲形成。该坳陷的发生和发展, 严格受东部鲁甸---哀牢山深断裂和西部澜沧江深断裂的控制。沿这两条深断裂带, 曾发生过多次强烈的构造运动、岩浆活动和变质作用, 从而形成了区内北北西向平行展布的点苍山---哀牢山变质带和崇山---澜沧江变质带。两变质带的变质岩类十分复杂, 深浅变质岩均有。深变质岩的时代很可能属中一晚元古代, 而部分中一浅变质岩为古生代和晚三叠世及侏

adams中函数用法

Adams常用函数 step可能是最常用的: step(time,0,0,1,50)+ step(time,4,0,6,-100)+ step(tme,9,0,10,50) 函数原形STEP(A,x1,h1,x2,h2) 解释：由数组A的x值，生成区间（x1，h1）至（x2，h2）之间的阶梯曲线，返回y值的数据。举个常用的例子。比如STEP(time,1,0,2,100) time在adams中是个递增的变量，相当于一个数组。那么step的返回值就是随着time变化的值。这个例子将表示在time从（1，2）的过程中，返回值将从0，100。看看例子，两个小球，一个使用step 函数设置了位移，另外一个是参考。当然，这个变化过程，adams使用了缓和的图形，从其位移图中可以看出来。step既然是个返回值，就可以使用加减法了。如上例，如果设置下面的小球的位移如下：STEP(time,1,0,2,100)+step(time,2,0,3,400)+step(time,3,0,4,-200) 1.以前用过碰撞函数，有单向和双向函数的区分，其中系统的球面等碰撞为其特例！ IMPACT (Displacement Variable, Veloci t y Variable, Trigger for Displacement Variable, Stiffness Coefficient, Stiffness Force Exponent, Damping Coefficient, Damping Ramp-up Distance) BISTOP (Displacement Variable, Velocity Variable, Low Trigger for Displacement Variable, High Trigger for Displacement Variable, Stiffness Coefficient, Stiffness Force Exponent, Damping Coefficient, Damping Ramp-up Distance) 2.if函数这个函数最好不要使用，他的使用会带来突变，会使运算的时候不收敛。不过应急的时候还是可以一用。 if(time-1:1,0,if(time-2:0,-1,-1)) IF(Expression1: Expression2, Expression3, Expression4) adams要计算Expression1的值：如果他的值小于0，则执行Expression2语句，如果Expression1的值等于0，则执行Expression3语句，如果Expression1的值大于0，则执行Expression4语句我得if语句的意思是：如果时间小于1的时候，加速度为1，如果时间为1，加速度为0，如果时间大于1小于2，则加速度为0，如果时间大于、等于2则，加速度为-1 4. 我得一个想法就是利用sign函数构造比较常用的是给机构加上一个与运动方向相反的作用力等等可以先测量施加力对象的运动速度，然后利用速度的变化，插入measure到sign函数里面就可以获得与运动方向相反的作用力

剖面测制及1：2000、1：10000地质测量汇编

剖面测制及1：2000、1：10000地质测量第一节剖面测制一、测制剖面的目的剖面测制是区域地质和矿区地质测量工作中的基础工作，一般放在地质填图工作的初始阶段即设计阶段进行，个别放在后期阶段进行，应依测区实际情况而定，按需要补测一定数量的剖面。地质普查和区域地质调查中的地质剖面可分为：（一）地层剖面：其目的是通过研究岩石物质及矿物成分、结构构造、古生物特征及组合关系、含矿性、标准层、沉积建造、地层组合、变质程度等。建立地层层序、查清厚度及其变化，接触关系，确定填图单位。（二）构造剖面：是着重研究区内地层及岩石在外力作用下产生的形变，如褶皱、断裂、节理、劈理、糜棱岩带（韧剪带）的特征、类型、规模、产状、力学性质和序次、组合及复合关系。对研究区域构造的剖面，要通过主干构造及典型的构造单元。（三）侵入岩剖面：主要是研究侵入岩的矿物成分、含量及组合、结构构造、含矿性、同化混染、接触蚀变作用、原生及次生构造、侵入体与围岩的接触关系、岩相变化特征、侵入期次、时代及侵入体与成矿的关系。确定侵入体中单元划分。（四）第四系剖面：研究第四纪沉积物的特征、成因类型及含矿性，时代，地层厚度及变化特征、新构运动及其表现形式。（五）火山岩剖面：研究火山岩的岩性特征、与上、下地层的接触关系、火山岩中沉积夹层的建造、生物特征；火山岩的喷民旋廻、喷发韵律，火山岩的原生构造和次生构造，确定火山岩的喷发形式、火山机构和构造。矿区勘探线剖面：分铅直剖面和水平剖面，此处仅指铅直剖面。在布设勘探剖面时，要照顾到整个矿床的各个地段，或兼顾相邻矿床。剖面线垂直矿体（床）走向线，间距一般与勘探网度一致。勘探线剖面主要反映矿体与围岩之间的界线，矿体中各种矿石自然类型和工业品级的界线，各种岩石之间的界线，各种构造界线；矿体的数量、分布、形状、大小、产状、厚度、矿石的自然类型和工业品级；构造控制和构造破坏等。剖面上标出探矿工程的种类、数量、位置、取样资料，从而可反映出勘探工作的工程控制程度、矿体圈定的合理程度、各地段的储量级别。二、剖面选择和布置原则地层剖面选择：应选在地层发育完整、基岩露头良好、构造简单、变质程度浅的地段。若露头不好或因构造影响，致使地层不全、界线不清时，可测制补充性的小辅助剖面。剖面布置：应基本垂直区域地层走向。地质构造复杂地区，剖面线方向和地层走向夹角不小于60度。若地层产状平缓，其剖面宜布置在地形陡坡处。三、测制剖面的基本方法和要求（一）剖面踏勘：在剖面线基本选定之后，应沿线进行踏勘。了解露头连续状况、构造形态、岩性特征、地层组合、侵入岩的分布、种类、岩性岩相变化、接触关系、初步了解地层单元及填图单元的划分位置、化石层位、重要样品采集地点等。在此基础上确定总导线方位、剖面测制中导线通过的具体部位，需平移的地段和必须工程揭露的地区，以及工作中的住地和各住站的时间。（二）剖面测制中人员分工野外工作一般需要5-8人。人员大致分工为：地质观察、分层兼记录1人作自然剖面、掌平面图（航片）1人前测手兼填记录表1人后测手兼标本采集1人放射性测量1人若人员充足时，记录和样品采集均可由专人负责。若测制古生物地层剖面，最好古生物鉴定人员参加，变质岩地层剖面最好岩矿鉴定人员参加，以指导化石、薄片的采集工作。

adams初级设置教程

1、ADAMS中的单位的问题开始的时候需要为模型设置单位。在所有的预置单位系统中,时间单位是秒,角度是度。可设置: MMKS--设置长度为千米,质量为千克,力为牛顿。 MKS—设置长度为米,质量为千克,力为牛顿。 CGS—设置长度为厘米,质量为克,力为达因。 IPS—设置长度为英寸,质量为斯勒格(slug),力为磅。 2、如何永久改变ADAMS的启动路径？在ADAMS启动后，每次更改路径很费时，我们习惯将自己的文件存在某一文件夹下；事实上，在Adams的快捷方式上右击鼠标，选属性，再在起始位置上输入你想要得路径就可以了。 3、关于ADAMS的坐标系的问题。当第一次启动ADAMs/View时,在窗口的左下角显示了一个三视坐标轴。该坐标轴为模型数据库的全局坐标系。缺省情况下,ADAMS/View用笛卡儿坐标系作为全局坐标系。ADAMS/View将全局坐标系固定在地面上。当创建零件时,ADAMS/View给每个零件分配一个坐标系,也就是局部坐标系。零件的局部坐标系随着零件一起移动。局部坐标系可以方便地定义物体的位置,ADAMS/View也可返回如零件的位置——零件局部坐标系相对于全局坐标系的位移的仿真结果。局部坐标系使得对物体上的几何体和点的描述比较方便。物体坐标系不太容易理解。你可以自己建一个ｐａｒｔ，通过移动它的位置来体会。 4、关于物体的位置和方向的修改可以有两种途径修改物体的位置和方向，一种是修改物体的局部坐标系的位置，也就是通过ＭＯＤＩＦＹ物体的ｐｏｓｉｔｉｏｎ属性；令一种方法就是修改物体在局部坐标系中的位置，可以通过修改控制物体的关键点来实现。我感觉这两种方法的结果是不同的，但是对于仿真过程来说，物体的位置就是质心的位置，所以对于仿真是一样的。

地质剖面图具体做法

实测地质剖面探矿者第一节实测剖面的目的及剖面位置的选择在某一地段内，沿一定方位实际测量和编制地质剖面图是一项重要的基础地质研究工作，也是对工作区内地层时代、层序、岩性特征、厚度、古生物演化特征、含矿层位和接触关系等进行综合研究的手段。在实测剖面工作中，凡是剖面线所经过的所有地质现象都要进行观察描述；各种地质数据和资料都要进行测量和收集；所涉及的地质问题都要详细进行研究。包括沿剖面线的地形变化；各时代地层的岩性特征及厚度；古生物化石层位及所含化石的种属特点；地层的接触关系；系统采集岩石标本及化石标本，采集各种分析样品待室内进行分析研究；有时要有专门人员进行地球物理及放射性测量等项工作。在此基础上，进行该区地质发展史的研究，以恢复古地理、古气候的特征，推断地壳运动的时期及特点，通过不同地质剖面的对比，研究同一时期不同地区的地质环境的变化等等。因此许多专门性的研究工作也都要通过实测一定数量的地质剖面来完成。在地质测量工作中，通过实测剖面系统掌握测区内上述资料的基础上，详细而准确地划分地层，确定填图单位，明确分层标志，为顺利开展地质测量作好基础工作。在踏勘测区的基础上，选择几条典型的剖面进行实测和研究，是地质测量工作的重要内容。为了使实测剖面顺利而有效地进行，选择好剖面线的位置是很重要的。选择剖面线有以下几点要求： 1.剖面线要通过区内所有地层，也就是说，在剖面线最短的情况下，通过的地层越全越好。剖面线应尽可能垂直于岩层走向。有时一条剖面不能包括所有地层，这时可分几个剖面进行测量，然后综合成一个连续剖面。所测每一时代地层最好要有顶面和底面，选择发育好、厚度最大的地段。以解决地层问题为目的的剖面，最好选择结构比较简单，尽可能不受断层、褶皱及岩体干扰的剖面。如果以解决构造问题为主，所选剖面应反映测区的主要构造特征，剖面线要垂直主要的褶皱轴线和断层走向。 2.剖面线经过地段露头要好，尽可能选择连续山脊或沟谷。避开障碍物，减少平移。为使制图整理方便，剖面线尽量取直，避免拐折太多。 3.根据对剖面研究的精度要求，确定剖面比例尺。如果要求将出露1m宽的岩性单位划分并表示出来，就应选取1︰1000的比例尺绘制；如果要求将出露2m宽的岩性单位划分并表示出来，则应选取1︰2000的比例尺绘制等等。所以，在实测剖面过程中，凡是在图上能表示1mm宽度的岩性单位都要划分出来，而有

adams函数

adams 函数 ADAMS/View 运行函数及ADAMS/Solver 函数 2008-04-18 04:54 3 ADAMS/View 运行函数及ADAMS/Solver 函数 ADAMS/View 运行函数能够表明定义系统行为的仿真状态间的数学关系。在ADAMS/ View 中将这些运行函数与其他不同元素一同创建各种系统变量，这些函数大多数都以施加力和产生运动为目的。之后在仿真中进行解算时，ADAMS/ Solver 会用到这些变量函数并进行计算更新，在仿真过程中这些系统状态会发生改变，如随时间的改变而改变、随零件的移动而改变、施加的力以不同方式改变等。 3.1 位移函数（1）线位移函数 DX 返回位移矢量在坐标系X 轴方向的分量 DY 返回位移矢量在坐标系Y 轴方向的分量 DZ 返回位移矢量在坐标系Z 轴方向的分量 DM 返回位移距离（2）角位移函数 AX 返回一指定标架绕另一标架X 轴旋转的角度 AY 返回一指定标架绕另一标架Y 轴旋转的角度 AZ 返回一指定标架绕另一标架Z 轴旋转的角度（3）按313 顺序的角位移 PSI 按照313 旋转顺序,返回指定坐标系相对于参考坐标系的第一旋转角度 THETA 按照313 旋转顺序,返回指定坐标系相对于参考坐标系的第二旋转角度 PHI 按照313 旋转系列,返回指定坐标系相对于参考坐标系的第三旋转角度（4）按照321 顺序的角位移 YAW 按照321 旋转顺序,返回指定坐标系相对于参考坐标系的第一旋转角度 PITCH 按照321 旋转顺序,返回指定坐标系相对于参考坐标系的第二旋转角度的相反数 ROLL 按照321 旋转顺序,返回指定坐标系相对于参考坐标系的第三旋转角度 3.2 速度函数（1）线速度函数 VX 返回两标架相对于指定坐标系的速度矢量差在X 轴的分量 VY 返回两标架相对于指定坐标系的速度矢量差在Y 轴的分量 VZ 返回两标架相对于指定坐标系的速度矢量差在Z 轴的分量 VM 返回两标架相对于指定坐标系的速度矢量差的幅值 VR 返回两标架的径向相对速度（2）角速度函数 WX 返回两标架的角速度矢量差在X 轴的分量

地质勘探测量

第12章地质勘探测量 12.1 勘探工程测量 12.1.1 概述矿产资源的地质勘探包括矿产普查和矿产勘探。其中矿产普查分为初步普查和详细普查，矿产勘探又分为初步勘探和详细勘查（精查)。在上述四个阶段中都要进行勘探工程，并需进行相应的测量工作，包括勘探工程测量、地质剖面测量和地质填图测量，其主要任务是：（1）为地质勘探工程设计提供测量资料；（2）根据设计在实地对勘探工程进行定位和定线，并测量已竣工工程的位置；（3）为研究地层构造、编写地质报告和储量计算提供有关测量资料。 12.1.2 勘探线与勘探网的测设 12.1.2.1 勘探线与勘探网的布设形式勘探线、勘探网的设计必须由地质人员通过现场实地踏勘后，依据地形条件和矿体走向来确定。勘探线的布设形式如图12-1所示，斜线区域是矿体的分布范围，曲线是地形等高线，编号为0-0'，1-1'……的单线表示勘探线，它是一组等间距的平行线，一般垂直于矿体的勘探网是由两组勘探线相交而成的，其形状和密度依据矿床的种类和产状而确定，通常布设成正方形、菱形和矩形等。为了控制勘探线和勘探网的测设精度，须遵循由整体到局部的原则，首先沿矿体走向布设一条“基线”，然后在此基础上布设其他勘探线。图12-2中M、N即为基线，基线两端点MN应与高级控制点连接。勘探网的编号以分数形式表示，分母代表线号，分子代表点号。以通过基点P的零号勘探线为界，西边的勘探线用奇数号表示，东边的则用偶数号表示；以基线为界，以北的点用偶数号，以南的点用奇数号表示。

已知控制点坐标，计算出测设所需的水平角和水平距离。然后依据这些测设数据采用常规测设方法，将基点M、N、P标定于实地。当基线两端点M、N和基点P初步确定后，应将经纬仪安置在其中任一点上检查三点是否在一条直线上。如果误差在允许范围内，则在基线两端点M、N埋设标石。然后采用单三角形或前方交会等方法，重新测定其坐标，求出它们与设计坐标的差值，若小于1/2000，可取其平均值作为最终坐标。否则应进行检查或重测。 12.1.2.3 勘探线、勘探网的测设勘探线、勘探网的测设就是将基线与勘探线上的工程点测设于实地。常规的测设方法是：在基点P安置经纬仪，定出基线方向，按设计给定的勘探线间距，采用钢尺量距或全站仪测距的方法定出各勘探线在基线上的交叉点（如图12-2中的0 2 、 4 、 6 、 8 和 1 、 3 、 0 5、 7 等），然后分别在这些点上安置经纬仪，后视基线点M、N、P，拨水平角? 90或? 270，依据设计给定的勘探线上工程点的点距，依次将各工程点测设于实地，即得到各组勘探线。将勘探线上的工程点测设于实地后，应埋设标志并编号。 12.1.2.4 高程测量在基线端点和基点测设于实地后，用三角高程的方法测量其高程。实际高程与设计高程如在规定限差之内，取其平均值即可，否则应查找原因。勘探线和勘探网高程的测定，可采用三角高程或水准测量方法，并布置成闭合或附合路线，以便于检核。当采用全站仪测设勘探线和勘探网时，可不再布设控制基线，而是在已有控制点的基础上，用测距导线建立一些加密控制点，均匀分布于勘探区内。然后依据这些加密控制点以及勘探线与勘探网的设计位置，采用极坐标法直接测设勘探工程点，同时用三角高程法测定

ADAMS函数使用精华

样条差值函数 Akima Fitting Method(AKISPL) 定义:由曲线或者曲面返回曲线的导数或者曲线的拟合值。通过Akima样条曲线拟合方法,使用一系列离散点来拟合曲线。格式:AKISPL(第一独立变量,第二独立变量,样条函数名,求导阶数) 自变量:第一独立变量(必须)--代表样条中第一独立变量的实数变量。第二独立变量(必须)-- 代表样条中第二独立变量的实数变量。样条函数名字(必须)—已存在的数据样条实体的名字,定义了用作拟合的一系列离散点。求导阶树(可选)—在求离散点时用作求导的阶树。其合法值为: *0—返回曲线坐标值。 *1—返回一阶导数值。 *2—返回二阶导数值。注意:当拟合曲面时,不必指明Derivative Order(求导阶数)。例子:某样条曲线,spline_1,其定义的离散点如下表所示。使用Akima样条拟合方法将这些离散点生成拟合函数。既然样条曲线定义的是曲线而不是曲面, 因此, 将Second Independent Variable(第二独立变量)设置为零。在下列例子中,给出了独立变量的值和数据,AKISPL返回拟合值: f = AKISPL(DX(marker_1, marker_2, marker_2), 0, spline_1) 由以上拟合点生成的样条曲线如下图所示:

CURVE 定义:CURVE 函数定义了一条B 样条曲线或者以CURVE 声明创建的用户自定义曲线。格式: CURVE (alpha, iord, comp, id) 自变量:alpha —确定独立变量α的值的实变量,其中CURVE 函数计算曲线。如果曲线是以CURVE 计算的B 样条曲线, α的取值范围为11-≤≤α。如果曲线是通过CURSUB 计算得出,alpha 的去值范围为MAXPAR MINPAR ≤≤α。 Iord —定义CURVE 函数中求导阶树的整数值。其合法值为 *0—返回曲线坐标。 *1—返回一阶偏导。 *2—返回二阶偏导。 Comp —定义CURVE 函数中分量的整数变量。其合法值为: *1—返回x 坐标值或者其导数值。 *2—返回y 坐标值或者其导数值。 *3—返回z 坐标值或者其导数值。自变量iord 和icomp 组合在一起可以让你获得下面九个值的任何一个: Id —定义CURVE 中标志符的整数变量。

实测地质剖面方法及地质填图要求

实测地层剖面为了对测区的地层情况有准确的了解，选择出露较好的典型地层剖面进行实际测量。（一）小组成员共同承担的任务 1.确定剖面起、止点, 将其准确标定在地形图上并标上地质点号剖面起、止点按地质填图地质点号统一编号，并在剖面线上用油漆做上醒目的标记。确定剖面起、止点通常采用三点交汇法并根据地形、地物加以校正。目前多采用卫星定位系统——GPS进行定位。确定剖面起、止点的原则：剖面起点要放在所测地层的下伏层位中，终点要放在所测地层的上覆层位中。例如：所要实测的地层是石炭系（C），起点要放在泥盆系（D）的顶部，终点要放在二叠系（P）的底部。如下图： 2.划分地层，将分层界线和分层号标在剖面线上地层划分的主要依据是地层的岩性特征，岩层剖面上岩石的颜色、结构、构造、成分或岩石组合规律等等方面的差异都可以作为分层标志。实测剖面所划分出的层，可以是单一岩性层，也可以是有规律组合在一起的复合岩性层。所划分出的每一层与上、下相邻层的宏观岩性特征应有较明显的差异，易于识别。复合岩性层的的组合规律主要有①夹层型（以一种岩性为主夹有其它岩性）；②互层型（由两种岩性交互产出）；③韵律型（三种或三种以上岩性顺序排列、重复出现）。地层划分的精度地层划分的精度(即：分层厚度)与所选定的比例尺有关，两者的关系如下：实测剖面分层精度与比例尺的关系

注: 最小分层厚度等于实测地层剖面图或柱状图上1mm所代表的地层厚度，最大分层厚度等于实测地层剖面图或柱状图上1cm 所代表的地层厚度。分层厚度的下限通常为自然岩层厚度。地层划分时应重视的问题地层划分时应重视有意义的特殊岩层，例如底砾岩层、古土壤层、含矿层、化石富集层、岩性独特的标志层等等，对于这些岩层，即使厚度不大也应单独分层，在剖面图和柱状图上予以夸大表示（可夸大到1mm）。 3.寻找化石应逐层依次寻找化石，将找到的化石顺序编号，并在化石发现地点用油漆做上标记。·根据小组成员的多少可作如下分工（见下表）：实测地层剖面人员分工 1. 前、后测手的任务 ①在已经确定的剖面线上，选择导线点，并做上标记（标注导线点号）。导线点的选择原则是：导线点应选择在地形明显起伏或剖面方向转折处以及剖面的起点和终点。导线点号的编码，由剖面起点至终点依次为0、1、2、3、……。 ②丈量导线距（斜坡距） ③测量导线方向：导线方向指的是导线起点至导线终点的方向。前、后测手共同测量，两者测量结果若相差太大，应重测；若相差不大，则取两者的平均值。

第三章_大比例尺地质填图和地质剖面测量工作方法

第三章1:10000以上比例尺地质填图和地质剖面测量工作方法第一节地质填图方法经过野外地质踏勘和野外实测剖面之后，在野外把各种地质、矿产现象用一定的符号勾绘在地形图上的过程。地质、矿产现象主要包括各时代的沉积岩、变质岩、岩浆岩及各种褶皱、断裂构造、矿体及各种矿化标志。野外地质填图的主要任务是进行路线地质调查，研究地质体的空间形态、相互关系和变化，填制地质图。由于分别以沉积岩分布为主、以岩浆岩分布为主及以变质岩分布为主的地区，其岩性特征及各种地质条件都有差异，因此，在这些地区的填图方法、内容等虽有大体相同或相似但也有所差别。野外地质填图工作，包括了观察路线的选择和布置，观察点的标定、内容观察和描述，野外地质图的勾绘及各种标本样品的采集和整理等内容。野外地质填图的目的任务1、1∶10000～1∶25000 地质填图（以下简称填图）的目的任务是：了解测区地质构造背景和成矿地质条件及区域成矿规律，扩大矿床（区）远景。2、1∶5000～1∶1000 填图的目的任务是全面而详细研究矿床（区）地层、岩石、构造特征；查明矿体分布形态、规模、产状、矿石质量、矿石类型及其空间分布；了解矿体与围岩的关系及围岩蚀变等。为探矿工程布置、储量计算提供矿区基础地质资料。一、观察路线布置填图工作应贯彻从已知到未知的原则。首先将实测地质剖面及确定的填图单元界线、断层线、侵入体界线、矿层顶底板界线、产状等的位置，绘到手图上，再从实测地质剖面两侧逐渐展开。 1 穿越法填图以手图上实测剖面线为起点，按照填图精度要求的观察线距离，垂直（或大

致垂直）岩层走向布置观察线。观察路线要根据填图精度考虑点线距，还要考虑基岩出露情况。 2 追索法填图选择标志层、含矿层或矿体、蚀变带，主要断层（或继裂带）等采用沿走向追索填图。观察路线一般采用“之”字形布置，以控制其顶底界线和了解变化情况。二、地质点布置地质点主要分为基本点、加密点、岩性产状点三类 1 基本点（主要点）：是控制测区地质界线和基本构造形态而布置的观察点。应布置在测区填图单元的界线、含矿层或矿体界线、蚀变带界线、岩体界线、断层面及褶皱轴等位置上。该类观察点要求作详细的文字记录（必要时加作放大素描图）。 2 加密点：为进一步控制地质界线和构造形态的变化，同时满足观察点密度要求，在基本观察点之间沿地质界线加密布置的观察点。该类观察点可只作简要的文字记录。 3 岩性或产状点：为控制和了解地质界线之间岩层产状变化及岩性特征、满足观察点密度和数量而布置的观察点。对该类观察点只需记录岩层产状和岩性特征。三、地质点密度及数量 1 地质点布置的密度及数量应根据填图比例尺大小、构造复杂程度、基岩出露情况、自然地理条件等因素确定，见表。地质点密度及数量（正测精度）表填图比例尺地质界线每平方公里地质点数（个）

adams个别问题总结

Adams个别问题总结 1、如何永久改变ADAMS的启动路径在ADAMS启动后，每次更改路径很费时，我们习惯将自己的文件存在某一文件夹下；事实上，在Adams的快捷方式上右击鼠标，选属性，再在起始位置上输入你想要得路径就可以了。 2、ADAMS中的单位的问题开始的时候需要为模型设置单位。在所有的预置单位系统中,时间单位是秒,角度是度。可设置: MMKS--设置长度为千米,质量为千克,力为牛顿。 MKS—设置长度为米,质量为千克,力为牛顿。 CGS—设置长度为厘米,质量为克,力为达因。 IPS—设置长度为英寸,质量为斯勒格(slug),力为磅。在模型运行的过程中也可以改变单位系统的设定。还可以在文本框中使用自己的单位，比如默认的角度单位度时可以使用Ｒ表示弧度。我感觉在ADAMS 内部好像是把所有的带单位的输入量都转换成统一的单位了。 3、关于ADAMS的坐标系的问题。当第一次启动ADAMs/View时,在窗口的左下角显示了一个三视坐标轴。该坐标轴为模型数据库的全局坐标系。缺省情况下,ADAMS/View用笛卡儿坐标系作为全局坐标系。ADAMS/View将全局坐标系固定在地面上。当创建零件时,ADAMS/View给每个零件分配一个坐标系,也就是局部坐标系。零件的局部坐标系随着零件一起移动。局部坐标系可以方便地定义物体的位置,ADAMS/View也可返回如零件的位置——零件局部坐标系相对于全局坐标系的位移的仿真结果。局部坐标系使得对物体上的几何体和点的描述比较方便。物体坐标系不太容易理解。你可以自己建一个part，通过移动它的位置来体会。4、关于物体的位置和方向的修改可以有两种途径修改物体的位置和方向，一种是修改物体的局部坐标系的位置，也就是通过modify物体的position属性；令一种方法就是修改物体在局部坐标系中的位置，可以通过修改控制物体的关键点来实现。我感觉这两种方法的结果是不同的，但是对于仿真过程来说，物体的位置就是质心的位置，所以对于仿真是一样的。 5、关于ADAMS中方向的描述。对于初学的人来说，方向的描述不太容易理解。之前我们都是用方向余弦之类的量来描述方向的。在ADAMS中，为了求解方程是计算的方便，使用欧拉角来描述方向。就是用绕坐标轴转过的角度来定义。旋转的旋转轴可以自己定义，默认使用313，也就是先绕ｚ轴，再绕ｘ轴，再绕ｚ轴。 6、Marker点与Pointer点区别