Asynchronous collision integrators: Explicit treatment of unilateral contact with friction and nodal restraints

Wolff, Sebastian; Bucher, Christian

doi:10.1002/nme.4516

Cited by 7 publications

(4 citation statements)

References 40 publications

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“…Therefore, testing of the VSRMM for crash and drop tests is promising. Further potential areas of application of the VSRMM may be dynamic relaxation [45], error estimation of eigenvalues [23,46,47], asynchronous variational integrators (AVI) with non-lumped mass matrices (usual AVI use the LMM approximation [48][49][50][51][52]), reduction of the dispersion error via customization of the RMM and preconditioning for other SMS techniques.…”

Section: Discussionmentioning

confidence: 99%

Direct and sparse construction of consistent inverse mass matrices: general variational formulation and application to selective mass scaling

Tkachuk

Bischoff

2014

Numerical Meth Engineering

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Classical explicit finite element formulations rely on lumped mass matrices. A diagonalized mass matrix enables a trivial computation of the acceleration vector from the force vector. Recently, non-diagonal mass matrices for explicit finite element analysis (FEA) have received attention due to the selective mass scaling (SMS) technique. SMS allows larger time step sizes without substantial loss of accuracy. However, an expensive solution for accelerations is required at each time step. In the present study, this problem is solved by directly constructing the inverse mass matrix. First, a consistent and sparse inverse mass matrix is built from the modified Hamiltons principle with independent displacement and momentum variables. Usage of biorthogonal bases for momentum allows elimination of momentum unknowns without matrix inversions and directly yields the inverse mass matrix denoted here as reciprocal mass matrix (RMM). Secondly, a variational mass scaling technique is applied to the RMM. It is based on the penalized Hamiltons principle with an additional velocity variable and a free parameter. Using element-wise bases for velocity and a local elimination yields variationally scaled RMM. Thirdly, examples illustrating the efficiency of the proposed method for simplex elements are presented and discussed.A. TKACHUK AND M. BISCHOFF Several algebraic methods for SMS are proposed in the literature. Mass penalty in thickness direction of solid-shell finite elements is proposed in [2,3]. This method adds artificial mass to the LMM for a relative motion in thickness direction for the nodes in the stacks of solid-shells. Such algebraic blocks reduce the highest thickness modes of the structure and at the same time are orthogonal to the bending modes, which allows accurate solutions for thin-walled structures. Stiffness proportional mass scaling ( ı D˛K) is described in [1,[4][5][6]. This method is accurate and allows preservation of the eigenvectors of the structure, but in case of non-linear problems, it requires reassembly of the scaled mass matrix for several times during the computation, because the stiffness matrix changes under large rotations and deformations [5]. The overhead introduced by reassembly is the main disadvantage of stiffness proportional mass scaling and the reason for not implementing the method in commertial finite element (FE) codes. This problem is partially resolved by the method described by Olovsson in [1]. This method uses an algebraically built template for added mass ı that does not change upon deformation and rotations. The kernel of this added mass ı includes the translational rigid body modes of individual elements, which mimics the stiffness proportional mass scaling. As a result of such a construction, the translational mass of individual elements is preserved. In addition, the method is easily implementable, and it is available in commercial codes, for example, LS-DYNA and RADIOSS. The implementation details are given in [7,8]. Further algebraic SMS methods scale the inertia of incom...

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Section: Discussionmentioning

confidence: 99%

Direct and sparse construction of consistent inverse mass matrices: general variational formulation and application to selective mass scaling

Tkachuk

Bischoff

2014

Numerical Meth Engineering

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“…In (Fetecau et al 2003b;Fetecau 2003) the classical theory of (smooth) Lagrangian mechanics is extended to the nonsmooth case in order to include collisions and the foundations of the multisymplectic formulation of nonsmooth continuum mechanics are presented in Fetecau et al (2003a). An example of asynchronous collision integrators can be consulted in Wolff and Bucher (2013) and an application to polymer chains in (Leyendecker et al 2012). In (Ryckman and Lew 2010 a new explicit dynamic contact algorithm that takes advantage of a variational asynchronous time integrator is formulated.…”

Section: Variational Integrationmentioning

confidence: 99%

A Brief Introduction to Variational Integrators

Lew

2016

Structure-Preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics

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In this chapter, a brief introduction to the formulation of variational methods for finite-dimensional Lagrangian systems is presented. To this end, the first two sections focus on describing the Lagrangian and Hamiltonian points of view of mechanics for systems evolving on manifolds. Special attention is paid to the construction of the Lagrangian function and to the role of Hamilton's variational principle in the deduction of the balance equations. The relation between the symmetries of the Lagrangian function and the existence of invariants of the dynamics along with the symplectic nature of the flow are also addressed. In the third section, the discussion turns towards the formulation of a time-discrete analogue of the theory. The cornerstone of such a construction is given by a discrete analogue of Hamilton's variational principle which provides a systematic procedure to construct discrete approximations to the exact trajectory of a mechanical system on both the configuration space and the phase space. The approximation properties and the geometric characteristics of the resulting discrete trajectories are explained. Finally, we apply the variational methodology to construct symplectic and momentum-conserving time integrators for two problems of practical interest in engineering and science.

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“…A notable global search algorithm is the position code algorithm [21], which transforms the process of sorting and searching in three dimensions into one within 1D array, and the computational complexity is reduced to O(N log 2 M) with the use of binary search method. The variants of the position code algorithm, such as those used in [22] and [23] with space filling curve, are more efficient but essentially have the same complexity on the computational cost. A more efficient one is the quick trace algorithm [24], which is a tree-like search algorithm and its computational complexity is further reduced to O(N log 4 M).…”

Section: Introductionmentioning

confidence: 99%

LC-Grid: a linear global contact search algorithm for finite element analysis

Lei

Miao

2014

Comput Mech

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The contact searching is computationally intensive and its memory requirement is highly demanding; therefore, it is significant to develop an efficient contact search algorithm with less memory required. In this paper, we propose an efficient global contact search algorithm with linear complexity in terms of computational cost and memory requirement for the finite element analysis of contact problems. This algorithm is named LC-Grid (Lei devised the algorithm and Chen implemented it). The contact space is decomposed; thereafter, all contact nodes and segments are firstly mapped onto layers, then onto rows and lastly onto cells. In each mapping level, the linked-list technique is used for the efficient storing and retrieval of contact nodes and segments. The contact detection is performed in each nonempty cell along non-empty rows in each non-empty layer, and moves to the next non-empty layer once a layer is completed. The use of migration strategy makes the algorithm insensitive to mesh size. The properties of this algorithm are investigated and numerically verified to be linearly proportional to the number of contact segments. Besides, the ideal ranges of two significant scale factors of cell size and buffer zone which strongly affect computational efficiency are determined via an illustrative example.

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Asynchronous collision integrators: Explicit treatment of unilateral contact with friction and nodal restraints

Cited by 7 publications

References 40 publications

Direct and sparse construction of consistent inverse mass matrices: general variational formulation and application to selective mass scaling

Direct and sparse construction of consistent inverse mass matrices: general variational formulation and application to selective mass scaling

A Brief Introduction to Variational Integrators

LC-Grid: a linear global contact search algorithm for finite element analysis

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