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提出一种有效的求解结构最小质量设计,同时满足动位移和动应力约束的二阶优化设计方法。在有限元法和纽马克法基础上导出一种高效的动应力、动位移对设计变量一阶导数和二阶导数的算法。建立含时间参数,以结构质量最小化为目标,同时满足动位移、动应力和设计变量约束的优化数学模型,通过积分型内点罚函数将含时间参数的不等式约束优化问题转变为一系列不含时间参数的无约束优化问题。利用动位移、动应力对设计变量一阶导数和二阶导数的信息计算内点罚函数的梯度和海森矩阵,利用梯度和海森矩阵构造求解优化设计问题高效有效的二阶优化算法。算例结果表明该文的优化设计方法能获得刚架结构的局部最优设计,优化的效率高于增广拉格朗日乘子法。
An effective second-order optimal design method is proposed to solve the design of the minimum mass of the structure and satisfy the dynamic displacement and dynamic stress constraints simultaneously. Based on the finite element method and the Newmark method, an efficient algorithm of dynamic and dynamic displacements for the first and second derivatives of design variables is derived. An optimization mathematical model with time parameters and minimizing the structural mass is proposed, which satisfies both the dynamic displacement, the dynamic stress and the design variable constraints. The integral penalty function is used to transform the inequality constrained optimization problem with time parameters into a series of Unconstrained Optimization with Time Parameters. The gradient and Hessian matrix of interior penalty function are calculated by using the information of dynamic displacement and dynamic stress on the first derivative and the second derivative of the design variables. The gradient and Hessian matrix are used to construct an efficient and effective second-order optimization algorithm for solving optimization design problems. The results show that the optimal design method of this paper can obtain the local optimal design of rigid frame structure, and the optimization efficiency is higher than that of augmented Lagrange multipliers.