Structural design sensitivity using boundary elements and polynomial response function |
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Authors: | Marcin Kamiński |
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Affiliation: | 1. Mechanics of Materials, Technical University of ?ód?, Al. Politechniki 6, 93-590, ?ód?, Poland
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Abstract: | This main issue of this paper is a conjunction of the structural design sensitivity analysis using the Boundary Element Method
with the polynomial response function determination. The procedure is so general that it enables sensitivity analysis for
potential and elasticity problems within both homogeneous and heterogeneous plane and 3D problems. The essential difference
with respect to the previous approaches like the Direct Differentiation Method or the Adjoint Variable Method is in discrete
evaluation of the structural response using the response polynomials of some state parameters and design variable as the independent
parameter. Such a determination is carried out via the several solutions of the given boundary value problem, where design
parameter mean value is regularly perturbed in each of the solutions to cover the closest neighborhood of this mean value.
Those few solutions make it possible to recover the polynomial response function from node-to node within the boundary elements,
so that further symbolic differentiation using MAPLE returns the sensitivity gradients particular values. The entire procedure
is tested here twice—first example deals with the homogeneous cantilever beam, where comparison against pure analytical differentiation
is done and, separately, for two-component composite cantilever, where such a comparison is made against the central difference
method linked with the same BEM solution. |
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Keywords: | |
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