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由含自重载荷功约束下桁架重量最小化问题的一阶极值条件导出功-重量分配准则,即结构重量应按外力功与自重载荷所做功之差的大小来正比分配才能达到最优。桁架拓扑优化的功射极法是依据不等式约束的Kuhn-Tucker极值条件以及射线步对功函数一阶偏导数的影响规律而构造的,它包括3个步骤,即:解析确定最佳射线步步长与乘子、求解功准则方程组。利用各设计变量的等比变化对不动点迭代求解式及其Jacobi矩阵的影响规律,证明所构造的求解式具有全局收敛性。基于功约束与应力约束的不相容性,可用应力比法对经拓扑优化的结构做进一步的优化。以多工况下三杆和十杆桁架结构为例验证所述方法的有效性。
The criterion of work-weight distribution is deduced from the first-order extreme conditions of minimizing the weight of trusses with self-contained load constraints. That is, the weight of structure should be proportional to the difference between the work of external force and self-weight load. The truss topology optimization power-law method is based on the inequality-constrained Kuhn-Tucker extremum conditions and the influence of the ray step on the first-order partial derivative of the work function. It consists of three steps, namely: resolving the best ray Step-length and multiplier, solving equations of equations. The influence law of the geometric change of each design variable on the iterative solution of fixed points and its Jacobi matrix is proved, which proves that the constructed solution has global convergence. Based on the incompatibility of work constraints and stress constraints, the topology-optimized structure can be further optimized by the stress ratio method. The effectiveness of the proposed method is validated by taking three and ten truss structures under multi-conditions.