Creation of Mechanism Using Linear Elastic Deformation

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  • 511 線形弾性変形を利用したメカニズムの創生

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This paper presents a numerical analysis method for boundary shape optimization problems of elastic continua to maximize the displacement on prescribed sub-boundaries by given external loads while maintaining stiffness. Mean displacement defined by integral of product of displacement and virtual boundary force on the prescribed sub-boundary is chosen as an objective functional. To maintain the stiffness, constraints for external works in two linear elastic problems are added to volume constraint. The shape gradient function of the problem is derived using the Lagrange multiplier method and the formula of material derivative. Reshaping was accomplished by the traction method. The Lagrange multipliers are determined based on the Kuhn-Tucker conditions by the Newton-Raphson method while the derivatives of the constraint functionals with respect to the Lagrange multipliers are evaluated using the finite differences. The presented method was applied to a three-dimensional gripper problem.

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