Keywords: parallel computing, MPI, GPU computing, finite strip method, geometrically nonlinear analysis.

A finite strip geometrically nonlinear analysis is presented for the problem of calculation of plates, bridges and various folded plate structures under arbitrary static loading. The procedure of deriving the nonlinear equations of balance, which are based on a Lagrangean formulation for moderately large deflections, is complex and general [1]. Within the constraints of the method, it has been shown to be superior to the finite element method in terms of data preparation, program complexity and execution time. However, the coupling of the series terms in the geometrical stiffness matrix calculation reduced the speed of calculation in an existing finite strip sequential program. Benefits of the parallelization of the finite strip method for linear analysis of structures have been noticed in 1997 [2]. In this paper we used parallelization of sequential algorithm for geometrically nonlinear analysis to achieve performance benefits.

Analyzing algorithm and existing sequential code, we identified strip stiffness matrix calculations as mutually independent. Also, we examined the execution profile of the sequential code and determined that over 90% of the execution time is spent calculating these matrices because an enormous number of arithmetic operations must be conducted for each strip.

Parallelization efforts are based on two different programming models (MPI and CUDA) for two different parallel architectures (loosely and tightly coupled). Examples show that substantial speedup can be achieved by distributing strip stiffness calculations on the computing cluster nodes and also by conducting some matrix linear algebra operations on a graphical processor unit on each node.

We argue that for efficient finite strips for geometrically nonlinear analysis parallelization, two types of parallel architectures are required: loosely and tightly coupled. These (different) architectures combined in a unified system, if utilized adequately, can achieve much better cost-performance trade-off. In such a system diversity of components characteristics is not an issue. On the contrary, different characteristics of different system parts are used to satisfy different requirements of different algorithm parts.

It is suggested that there is a significant class of problems similar to the one just presented, that can be parallelized more elegantly and more efficiently on adequately combined complementary hardware.

1

D.D. Milašinovic, "The Finite Strip Method in Computational Mechanics", Faculties of Civil Engineering, Subotica, Budapest, Belgrade, 1997.

2

H.-C. Chen, V. Byreddy, "Solving plate bending problems using finite strips on networked workstations", Computers & Structures, 62, 227-236, 1997. doi:10.1016/S0045-7949(96)00190-3

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