Singularity in structural optimization

Abstract

SUMMARYSingularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities in linear elastic structures have been identified in earlier papers, along with a proposition to alleviate the consequences of their presence. -3 These singularities were global in nature, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. This paper provides examples of these additional forms of singularities. It gives a framework in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress-displacement relations along with the compatibility conditions and/or the displacement-stress relations derived in the integrated force method of structural analysis. Methods for the elimination of the effects of these singularities are suggested and numerical illustrations are given.

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Significance of Strain Formulation in Theory of Solid Mechanics

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“…Benefits from the use of the completed strain formulation are being shown in continuum elasticity, [1][2][3][4][5][6] in finite element analysis, [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and in design optimization. [26][27][28][29][30][31][32][33][34][35][36] The theory of strengths of materials began with the cantilever experiment conducted by Galileo in 1632. 37 Several decades later the stress (σ) This contained two distinct sets of equations: the field equations τ ij, j + b i = 0, and boundary or traction conditions p i = τ ij n j .…”

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