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Research Papers

A Deflated Assembly Free Approach to Large-Scale Implicit Structural Dynamics

[+] Author and Article Information
Amir M. Mirzendehdel

Department of Mechanical Engineering,
University of Wisconsin-Madison,
Madison, WI 53706

Krishnan Suresh

Department of Mechanical Engineering,
University of Wisconsin-Madison,
Madison, WI 53706
e-mail: suresh@engr.wisc.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 27, 2014; final manuscript received November 12, 2014; published online April 9, 2015. Assoc. Editor: José L. Escalona.

J. Comput. Nonlinear Dynam 10(6), 061015 (Nov 01, 2015) (9 pages) Paper No: CND-14-1163; doi: 10.1115/1.4029110 History: Received June 27, 2014; Revised November 12, 2014; Online April 09, 2015

The primary computational bottle-neck in implicit structural dynamics is the repeated inversion of the underlying stiffness matrix. In this paper, a fast inversion technique is proposed by merging four distinct but complementary concepts: (1) voxelization with adaptive local refinement, (2) assembly-free (a.k.a. matrix-free or element-by-element) finite element analysis (FEA), (3) assembly-free deflated conjugate gradient (AF-DCG), and (4) multicore parallelization. In particular, we apply these concepts to the well-known Newmark-beta method, and the resulting AF-DCG is well-suited for large-scale problems. It can be easily ported to many-core central processing unit (CPU) and multicore graphics-programmable unit (GPU) architectures, as demonstrated through numerical experiments.

Copyright © 2015 by ASME
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Figures

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Fig. 1

An example of transient analysis of a thin elastic structure

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Fig. 2

An overview of the proposed method

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Fig. 3

Brute-force voxelization of the structure in Fig. 1

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Fig. 4

(a) Stress concentration and (b) local refinement

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Fig. 5

The regions of stress concentration can change during transient analysis. (a) t = 1 × 10−7 s, (b) t = 1 × 10−6 s, (c) t = 1 × 10−5 s.

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Fig. 6

(a) Finite element mesh and (b) agglomeration of mesh nodes into four groups

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Fig. 7

Deflected cantilever beam

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Fig. 8

Relative tip displacement (ansys)

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Fig. 9

Relative tip displacement (AF-DCG)

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Fig. 10

Run-time comparison of ansys versus AF-DCG

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Fig. 11

L-bracket geometry (dimensions in mm) and loading

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Fig. 12

Normalized stress for the L-bracket (ansys).

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Fig. 13

Normalized stress for the L-bracket (AF-DCG)

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Fig. 14

Rocker problem: (a) loading and (b) displacement

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Fig. 15

Time taken (s) by solidworks 2014 [26] direct and iterative solvers, as a function of the DOF

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Fig. 16

Memory consumed by solidworks 2014 [26] direct and iterative solvers, as a function of DOF

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Fig. 17

Faster convergence due to deflation

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Fig. 18

Battery holder geometry with small features

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Fig. 19

Battery holder's relative maximum stress

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Fig. 20

Battery holder: run-time comparison

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Fig. 21

Arduino MEGO 2560

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Fig. 22

Arduino MEGA 2560: voxel mesh

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Fig. 23

Arduino MEGA 2560: displacement field

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Fig. 24

Arduino MEGA 2560: run-time comparison of CPU and GPU

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Fig. 25

Arduino MEGA 2560: normalized maximum stress

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