Hamilton体系下混凝土壳体结构的基本方程及求解方法

基于极坐标下混凝土壳体结构的基本方程，根据结构力学与最优控制的模拟关系，利用径向坐标模拟为时间坐标，推导了Hamilton体系下混凝土壳体结构的状态方程；进而在辛体系下，采用本征向量展开法对系统进行了分析，并给出了相应的实际算例，其结果说明了文中方法的有效性和正确性。为此类结构的计算提供了一种新的求解途径。

A New Systematic Computational Methodology for Concrete Shell Structures

The research group at Dalian University of Technology , of which the first author has long been and is still a member, initiated a new systematic computational technology, utilizing the analogy between structural mechanics and control theory. We aim to extend this new approach to studying the structural performance of concrete structures. For quite a number of applications of shell structures, concrete instead of reinforced concrete, can be used. In this paper, the basic equations and solution approach of concrete shell structure are given by the above theoretical method under polar coordinate systems then, according to the analogy relations between computational structural mechanics and optimal control, in which the radial coordinate can be treated as time coordinate, and the state equations of the structural system are further established under the Harniltonian system. In symplectic space, the eigenvector expansion method is used to study the system, and the corresponding numerical example is given, which shows the validity and effectiveness of the proposed method.