• Journal of the Computational Structural Engineering Institute of Korea
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• v.35 no.6
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• pp.367-374
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• 2022

This papter presents the use of the automatic differential method based on the backpropagation method to obtain the design sensitivity and its application to topology optimization considering the stress constraints. Solving topology optimization problems with stress constraints is difficult owing to singularities, the local nature of stress constraints, and nonlinearity with respect to design variables. To solve the singularity problem, the stress relaxation technique is used, and p-norm for stress constraints is applied instead of local stresses for global stress measures. To overcome the nonlinearity of the design variables in stress constraint problems, it is important to analytically obtain the exact design sensitivity. In conventional topology optimization, design sensitivity is obtained efficiently and accurately using the adjoint variable method; however, obtaining the design sensitivity analytically and additionally solving the adjoint equation is difficult. To address this problem, the design sensitivity is obtained using a backpropagation technique that is used to determine optimal weights and biases in the artificial neural network, and it is applied to the topology optimization with the stress constraints. The backpropagation technique is used in automatic differentiation and can simplify the calculation of the design sensitivity for the objectives or constraint functions without complicated analytical derivations. In addition, the backpropagation process is more computationally efficient than solving adjoint equations in sensitivity calculations.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.3
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• pp.311-318
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• 2015

A nonlinear dynamic response structural optimization process is proposed for the television (TV) packing system that protects the damage from a drop situation using the equivalent static loads (ESLs). Topology optimization using ESLs is carried out for conceptual design, and shape optimization using stress ESLs for a virtual model is performed for detailed design. Stress ESLs are static loads that generate the same displacement as well as the stress fields of linear static analysis as those of nonlinear dynamic analysis. Thus, the response of nonlinear dynamic analysis can be utilized as a constraint in the linear static structural optimization. An actual example is solved to validate the process. The drop test of a television packaging system is analyzed by LS-DYNA, and NASTRAN is used for optimization.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.5
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• pp.441-449
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• 2015

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.

• Journal of the Korea Institute of Military Science and Technology
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• v.25 no.6
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• pp.561-571
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• 2022

An optical mirror assembly is an opto-mechanically coupled system as the optical and mechanical behaviors interact. In the assembly, a flexure mount attached to an optical mirror should be flexible in the radial direction, but rigid for the remaining degrees of freedom for supporting the mirror rigidly and suppressing the wavefront error of the optical mirror. This work presents an optimal design of the flexure mount using topology optimization with thermal stress constraint. By simplifying the optical mirror assembly into finite shell elements, topology optimization model was built for efficient design and good machinability. The stress at the boundary between the optical mirror and the mount together with the first natural frequency were applied as constraints for the optimization problem, while the objective function was set to minimize the strain energy. As a result, we obtained the optimal design of the flexure mount yielding the improved wavefront error, proper rigidity, and machinability.