基于非线性规划的对偶理论和函数的二阶台劳展得开、得到了一种有效的结构优化设计方法。它具有能用性、可自动判别临界约束集合、计算效率高和适用于大型结构系统等优点。基于虚功原理，导出了性状参数的一阶和二阶导数计算式。利用圣维原理，使性状参数二阶导数及相应的Hessian矩阵计算式大为简化。典型号算例的计算结果表明本方法是相当有效的。

By using approximation concepts, the objective function and constraint functions have been approximated by second and frist order Taylor series expanisons, respectively. A sequence of quadratic programming problems is thus obtained and than solved by quasi-analytical method based on the theory of nonlinear programming. Several typical problems have been teated. The results have shown satisfactory convergence and computational efficeieny.

回顾与分析了工程数值优化方法研究的发展历程，着重介绍与讨论了优化问题的几种数学列式、近似问题的保真度与近似函数，以及复杂优化问题的求解策略等。指出优化问题的对偶列式变式DFO P2V 2与高精度多点近似函数和二级近似概念结合而产生的数值优化解法，具有通用性，高的计算效率，并易于与市场现有分析软件结合使用等显著优点。

A two-level multipoint approximation concept is proposed. Based upon the values and the first-order derivatives of the critical constraint functions at the points obtained in the procedure of optimization, explicit functions approximating the primal constraint functions have been created. The nonlinearities of the approximate functions are controlled to be near those of the constraint functions in their expansion domains. Based on the principle above, the first-level sequence of explicitly approximate problems used to solve the primarily structural optimization problem are constructed. Each of them is approximated again by the second-level sequence of approximate problems, which are formed by using the linear Taylor series expansion and then solved efficiently with dual theory. Typical numerical examples including optimum design for trusses and frames are solved to illustrate the power of the present method. The computational results show that the method is very efficient and no intermediate/generalized design variable is required to be selected. It testifies to the adaptability and generality of the method for complex problems.

A new concept for complex structural optimization problem is presented. Based on investigation of the mechanical nature of the studied problem, a set of basic medchanical characteristies can be introduced as the generalized variables. A high-quality explicit first-level approximate problem FA is formed by first-order Taylor series expansion of the behaviour constraints in terms of the generalized variables. The FA is explicit but highly non-linear with respect ot deign variables. Thererfore, a second-leel approximation is introduced to solve the FA by considering a sequence of second-level approximate problem SA in the design variable space. This approac is a Two-Level Approximation Concept. Its appliation to space frame synthesis shows tis grasp of the mechanical natrue of the problem. The computational results for several examples show that the method presented in this paper is very efficeien.