分析FRP补强结构的状态空间有限元法

文章应用分区变分原理和状态空间有限元法分析FRP补强的层合板;在板的平面内划分有限元网格,根据混合变分原理分别建立层合板和补片的状态方程;沿厚度方向求解状态方程分别得到层合板和补片上、下表面之间的关系,再根据板与补片之间的协调条件建立补强结构的整体求解方程.该方法综合了状态空间法与有限元法的优点,如能同时满足层间位移和应力的连续条件和方便处理边界条件等.算例表明用所提出的方法求解补强结构是非常有效的.

Analysis of FRP reinforced structure based on state space finite element method

The region-wise variational principle and the state space finite element method are applied to analyze the composite laminated plate with the adhesive patch.The FE mesh is divided in the plane of the plate and the state equations for the composite plate and adhesive patch are established respectively based on the mixed variational principle.The relation between upper and bottom surfaces is obtained by solving the state equation through the thickness of the composite plate or adhesive patch.The entire equation for the reinforcement structure is established by using the compatible conditions between the composite plate and the adhesive patch.The present method has many merits inhereing in the state space method and the finite element method simultaneously.For example,the continuity conditions of displacements and stresses between the plies of the laminates are satisfied and boundary conditions of the plate can be treated easily.The numerical examples illustrate that the proposed method is very efficient for solving the problem of the reinforcement structure.