Non-parametric Shape Optimization Method For Thin-walled Structures Under Strength Criterion
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M. Shimoda, J. Tsuji & H. Azegami
This paper presents a numerical optimization method for shape design to improve the strength of thin-walled structures. A solution to maximum stress minimization problems subject to a volume constraint is proposed. With this solution, the optimal shape is obtained without any parameterization of the design variables for shape definition. It is assumed that the design domain is varied in the in-plane direction to maintain the curvatures of the initial shape. The problem is formulated as a non-parametric shape optimization problem. The shape gradient function is theoretically derived using the Lagrange multiplier method and the adjoint variable method. The traction method, which was proposed as a gradient method in Hilbert space, is applied to determine the smooth domain variation that minimizes the objective functional. The calculated results show the effectiveness and practical utility of the proposed solution in solving minmax shape optimization problems for the design of thin-walled structures under a strength criterion. Keywords: shell, shape optimization, traction method, structural optimization, optimal shape, non-parametric optimisation, minmax, adjoint variable. 1 Introduction Thin-walled structures such as plates and shells are characterized by their ability to efficiently bear externally applied forces by means of the resultant membrane stress and bending stress. One can find many examples of such structures in the natural world, including leaves, seashells, eggshells and beetle shells, among
shell, shape optimization, traction method, structural optimization, optimal shape, non-parametric optimisation, minmax, adjoint variable.