基于Newmark法敏度计算的刚架结构动力优化

DYNAMIC OPTIMIZATION OF FRAME STRUCTURES USING SENSITIVITY CALCULATION BASED ON NEWMARK METHOD

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。

This paper proposes an effective second-order optimal design method for minimizing the mass of structure and satisfying the dynamic displacement and stress constraints.An efficient algorithm of the first and second derivatives of dynamic displacement and stress with respect to design variables is formulated based on the finite element method and the Newmark method.The time-dependent mathematical model for achieving minimum mass design with the dynamic displacement,dynamic stress and design variable constraints is formulated.The inequality time-dependent constraint problem is converted into a sequence of appropriately formed time-independent unconstrained problems using the integral interior point penalty function method.Gradient and Hessian matrix of the integral interior point penalty function are also computed using the information of the first and second derivatives of dynamic displacement and dynamic stress with respect to design variables.The efficient and effective second-order optimal algorithm is constructed to solve the optimal design problem using the gradient and Hessian matrix.The numerical results show that the optimal design method proposed in this paper can obtain the local optimum design of frame structures and is more efficient than the augmented Lagrange multiplier method.