Umesha, P K
(2001)
*Parallel Computing Techniques for Analysis and Design Optimization of Large Structural Systems.*
Phd. Thesis thesis, Manipal Institute of Technology, Manipal.

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## Abstract

The implementation of the parallel algorithms for analysis and design optimization of structures was done using Computer-Adaptive Language as software platform. A parallel version of computer-adaptive language has been developed and implemented on message passing systems. A Graphic User Interface (GUI) for conceptual modelling of the structures has been developed using X-Windows and Motif toolkit under Unix environment. Several domain decomposition algorithms have been developed and integrated with this GUI for better choice of the partitioned domain. The Parallel finite element analysis has been carried out by dividing the domain into a number of sub-domains. Each of these sub-domains is assigned to one processor in the message passing parallel computer. The element stiffness formulation of each sub-domain and assembly are performed concurrently and then reduced by condensing out all the nodes except for the interface nodes leading to a reduced stiffness matrix and a reduced load vector. The reduced stiffness and load matrices are assembled in the master processor underthe master-slave configuration on parallel computer. The global system of equations is solved. The subsequent analysis, which involves the computation of sub-domain internalnodaldisplacements and stress recovery, is performed concurrently. In the structural optimization of truss structures, the volume of the structure is considered as objective function. The cross-sectional areas of bars are considered as design variables and the displacements, stresses and buckling stresses as constraints and the upper and lower limit of cross-sectional areas as side constraints. The newly devised multi level approaches for parallel design optimization of large structures are implemented for load. caseparallelism and sub-domain parallelism. Thedesign optimization of truss structures subjected to multiple loads was solved as a twolevel suboptimization problem. Here each load case is treated as an independent optimization task executed on a separate processor in parallel. Each analysis and design cycle on parallel processors is started with the same initial configuration. At the end of eachcycle, a single new configuration is arrived for all load cases by taking the envelope of each design variable at the second level. The maximum value of each design variable from different processors is taken as co-ordinating variables. In the sub-domain optimization technique, the original structure is divided into several subdomains. Each substructure can have independent design variables and a small number of (overlap) of design variables between subdomains must be provided. The parallel finite element analysis has been carried out to computethe stresses and nodal displacements. Sub-domain optimization has been carried outby considering sub-domain volume as the objective function and stresses in members withinthe sub-domain as local constraints and displacements in the whole structure as the globalconstraints. For each sub-domain, a unique set of design variables will be obtained resulting in a substructure volume. The design co-ordination takes place on the second levelfor the coupling design variables and the complete volume of the structure. In the design optimization of large structural systems with gradient-based optimization methods, sensitivity analysis, that is, the determination of the change of the objective function and the constraints with respect to the design variables, is the most time consuming computational process. Utilizing the parallel computational methods, the sensitivity analysis contributes the most to the speedup of structural optimization. Computation of sensitivities is characteristically uncoupled, so it is possible to calculate the gradients in parallel. Two levels of parallelisms are pursued in combination with a single-leveland a multilevel optimization. In a single level parallelism, the coefficients of gradients matrices of objective function, and of constraints for the complete structure are computed in parallel. In multi-level parallelism, a divide-and-conquer strategy is pursued. After the parallel finite element analysis, each processor computes .sub-domain displacements and constraint gradient matrixof that sub-domain. The computation of stress constraint gradient can be performed in parallel without any communication. The sub-domain gradient matrices are collected fromall processors and sequential optimization has been carried out. The sensitivities are computedusing analytical method and forward finite difference method. Performance of parallelalgorithms has been shown by working out several numerical examples. Ageometrically non-linear truss element has been developed using the updated Lagrangian method. The solution techniques like Newton-Raphson, modified Newton-Raphson and quasi-Newton methods (Broyden-Fletcher-Goldfarb-Shanno method) have been used for solving the non-linear system of equations. A parametric study by varying the degrees of freedom has been carried out. The algorithms for design optimization of geometrically non-linear truss structure are developed with parallel load case ·and parallel sensitivity calculation. The nodal displacements and stresses after non-linear analysis are used to evaluate constraints in the design optimization.

Item Type: | Thesis (Phd. Thesis) |
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Subjects: | Engineering > MIT Manipal > Civil Engineering |

Depositing User: | MIT Library |

Date Deposited: | 30 May 2014 06:19 |

Last Modified: | 07 Nov 2014 09:44 |

URI: | http://eprints.manipal.edu/id/eprint/138887 |

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