A Practical Solution To The Shape Optimization
Problem Of Solid Structures
Author(s)
M. Shimoda, S. Motora & H. Azegami
Abstract
This paper presents a practical optimization method for the shape design of solid
structures or 3-dimensional structures in order to obtain the optimal free
boundary shape without any parameterization of the shape for optimization. A
solution to the rigidity design problem of a solid structure under the assumption
that the Neumann boundary is allowed to vary is presented. The compliance is
minimized subject to a volume constraint and the state equation. Surface
tractions, body forces and hydrostatic pressure are applied on the specified
regions. This design problem is formulated as a non-parametric shape
optimization problem. The shape gradient function is theoretically derived using
the Lagrange multiplier method, the material derivative method and the adjoint
variable method. With the shape gradient function and the traction method that
was proposed by the authors as a gradient method in a Hilbert space, the smooth
optimal shape can be easily obtained. This solution is applied to four design
problems. The results obtained verified the effectiveness and practical utility of
the proposed method for the shape design of solid structures with variable
Neumann boundaries.
Keywords: solid structure, shape optimization, traction method, optimal shape,
non-parametric optimization, adjoint variable, material derivative.
Keywords
solid structure, shape optimization, traction method, optimal shape,
non-parametric optimization, adjoint variable, material derivative.
Related Book
Other papers in this volume
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