Solution to Shape Identification Problems in Thermoelastic Fields to Prescribe Von Mises Stress Distributions

Abstract

The present paper introduces a numerical analysis method for the shape identification problem to prescribe von Mises stress distributions on sub-domains in a thermoelastic field from the point of view of strength design. The square error integrals between the actual von Mises stress distributions and the prescribed distributions on the sub-domains are used as an objective functional. The shape gradient of the shape identification problem is derived theoretically using the adjoint variable method, the Lagrange multiplier method, and the formulae of the material derivative. Reshaping for the shape identification is accomplished using a traction method that was proposed as a solution to shape-optimization problems. The validity of the proposed method is confirmed based on the results of a 2D numerical analysis.