不确定载荷下的桁架结构拓扑优化

Truss topology optimization with uncertain loading scenarios

对带有不确定扰动载荷的桁架结构拓扑优化问题进行了研究.将不确定载荷表示成有界凸集,从而把不确定性问题转化为一个确定性问题.构造了凸集载荷下以体积为约束的柔度最小化模型,该优化模型的实质是在高维椭球内计算最大柔度最小问题.由于采用传统优化模型存在计算上的困难,对凸集载荷进行了数学处理,并据此构造了半定规划形式的优化模型以便求解.优化结果相对于给定载荷的刚度虽然略低,但对不确定的扰动载荷却具有一定的承载能力.算例表明通过半定规划法构造的考虑扰动载荷作用下的优化结果鲁棒性较佳,结构形式更接近于实际工程结构.

A new model of truss topology optimization （TTO） considering uncertain （ in size and direction） loading scenarios was presented. The uncertain loading was modeled as bounded convex sets, and the uncertain model was transformed to a deterministic model. The TTO was formulated as minimization of the compliance subject to volume constraints, and the nature of this type of optimization is to minimizing maximum compliance in high dimensional ellipsoid. The traditional model considering convex sets is hard to solve, and TTO with convex sets was modeled as semidefinite programming （SDP） to overcome this special difficulty. The compliance both to given loading scenarios and a small occasional was simultaneously optimized in SDP model and optimum result showed that the compliance of the truss were slightly reduced respect to given loads, but the optimum topology of the truss is more robust and more practical than that with non-uncertain loading scenarios from the engineering viewpoints.