Shape optimization of an elasto-perfectly plastic body
Shape optimization of an elasto-perfectly plastic body
复制标题
完美弹塑性体的形状优化
DOI：
10.21136/am.1987.104269
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发表时间：
1987
期刊：
影响因子：
--
通讯作者：
I. Hlavácek
中科院分区：
文献类型：
--
作者：
I. Hlavácek
在Prandtl-Reuss弹塑性模型范围内，解决了以下优化设计问题。给定物体的力和表面的力，要找到（二维）物体固定的边界的一部分，以便使平方屈服函数的积分最小。的状态问题制定的应力通过一个时间依赖的变分不等式。对于未知边界的分段线性近似的近似解，使用用于应力和向后时间差的分段常数三角形有限元。收敛的近似的最优设计问题的解决方案的证明。作为一个结果，最优边界的存在性得到了验证。
Within the range of Prandtl-Reuss model of elasto-plasticity the following optimal design problem is solved. Given body forces and surface tractions, a part of the boundary, where the (two-dimensional) body is fixed, is to be found, so as to minimize an integral of the squared yield function. The state problem is formulated in terms of stresses by means of a time-dependent variational inequality. For approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular finite elements for stress and backward differences in time are used. Convergence of the approximations to a solution of the optimal design problem is proven. As a consequance, the existence of an optimal boudary is verified.