网状扁壳与带肋扁壳组合结构的拟三层壳分析法

Three-Layer Shell Analogy Method for Analyzing Composite Structures Composed of Lattice Flat Shells and Rib Flat Shells

本文对网状扁壳与带肋扁壳共同工作的组合结构(可简称组合网状扁壳),采用连续化的拟三层壳的计算模型,按弹性小挠度薄壳理论进行分析计算,推导建立了混合法的基本方程式。由于这种构造上的拟三层壳在一般情况下不存在中面,因而壳体的薄膜内力、弯矩与薄膜应变,弯曲应变是耦合的,存在一个耦合矩阵,使得基本方程式比单层光面的符氏扁壳方程要复杂得多。对于周边简支的组合网状扁壳可求得基本方程式的解析解。文中对三向、四向组合网状扁壳进行了详细讨论,并指出了在特定条件下,可退化为一个当量的各向同性单层扁壳。对于一般网状扁壳的拟壳分析法及带肋扁壳的拟壳分析法分别属于本文的两种特殊情况。文中附有计算例题。

This paper presents a three-layer analogy method for analyzing composite structures composed of lattice flat shells and rib flat shells working interactively (called as composite lattice flat shell for short) .The basic equations are established by the composite method using the continual three-layer analogy model and elastic small deflection theory for thin shell analysis. Since this analogue by three-layer shell usually has no central curved surface in construction, the membrane internal forces and the moments are coupled with the membrane strains and bending strains and a coupling matrix shall appear in the basic equations which in the case of the composite lattice flat shells will be more complicated than those of the ordinary flat shells. The analytical solution to the basic equations of the composite lattice flat shell simply supported at its perimeter is given. Furthermore, this paper discusses three-direction and four-direction composite lattice flat shell in detail and points out that these shells can be simplified to an equivalent isotropic single-layer flat shell under specific conditions. The shell analogy method of lattice flat shell or rib flat shell is the special case of the proposed method. Numerical example is also included in the paper.