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1.引言 结构抗震优化设计的困难在于大部分约束条件都是设计变量的非线性隐函数,在用数学规划法优化时常需求隐式约束的动力灵敏度。如何克服这一难点,是人们研究动力优化的重点之一,迄今尚未很好地解决。 本文用序列二次规划研究了弯剪型多层刚架的抗震优化设计,较好地解决了上述问题。对于应力约束,用Taylor展开,取一阶项,对于位移约束,用图乘法把相对位移化为线性显式,从而避免了求算非线性隐式约束的动力灵敏度。把原变量的序列二次规划化为以Lagrange乘子为变量的线性互补问题,用Lemke方法求解。算例表明,结果是合理的,本文的方法是有效的。
1. Introduction The difficulty of structural anti-seismic optimal design is that most of the constraints are the nonlinear implicit functions of the design variables. In the optimization using mathematical programming, the dynamic sensitivity of implicit constraints is often required. How to overcome this difficulty is one of the focuses of people’s research on power optimization and has not yet been well resolved. In this paper, the seismic optimization design of the curved-shear multi-layer rigid frame is studied by using the sequential quadratic programming, and the above problems are solved. For stress constraints, use Taylor to expand, take first-order terms, for displacement constraints, use map multiplication to convert the relative displacement to linear explicit, thus avoiding the dynamic sensitivity of nonlinear implicit constraints. The sequence of the original variables is quadraticized into a linear complementarity problem with Lagrange multipliers and solved with the Lemke method. The example shows that the result is reasonable and the method in this paper is effective.