Topology Design Optimization of Plate Buckling Problems Considering Buckling Performance
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In this paper we perform a linearized buckling analysis using the Kirchhoff plate theory and the von Karman nonlinear strain-displacement relation. Design sensitivity analysis(DSA) expressions for plane elasticity and buckling problems are derived with respect to Young’s modulus and thickness. Using the design sensitivity, we can formulate the topology optimization method for minimizing the compliance and maximizing eigenvalues. We develop a topology optimization method applicable to plate buckling problems using the prestress for buckling analysis. Since the prestress is needed to assemble the stress matrix for buckling problem using the von Karman nonlinear strain, we introduced out-of-plane motion. The design variables are parameterized into normalized bulk material densities. The objective functions are the minimum compliance and the maximum eigenvalues and the constraint is the allowable volume. Through several numerical examples, the developed DSA method is verified to yield very accurate sensitivity results compared with the finite difference ones and the topology optimization yields physically meaningful results.
Abstract
In this paper we perform a linearized buckling analysis using the Kirchhoff plate theory and the von Karman nonlinear strain-displacement relation. Design sensitivity analysis(DSA) expressions for plane elasticity and buckling problems are derived with respect to Young’s modulus and thickness. Using the design sensitivity, we can formulate the topology optimization method for minimizing the compliance and maximizing eigenvalues. We develop a topology optimization method applicable to plate buckling problems using the prestress for buckling analysis. Since the prestress is needed to assemble the stress matrix for buckling problem using the von Karman nonlinear strain, we introduced out-of-plane motion. The design variables are parameterized into normalized bulk material densities. The objective functions are the minimum compliance and the maximum eigenvalues and the constraint is the allowable volume. Through several numerical examples, the developed DSA method is verified to yield very accurate sensitivity results compared with the finite difference ones and the topology optimization yields physically meaningful results.
참고문헌 (12)
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