基于混合状态变量的中厚板条形传递函数解

Strip Transfer Function Solution Based on Mixed State Vectors of Moderately Thick Plates

基于Mindlin板理论和改进的混合能量变分原理,建立了矩形区域中厚板问题的条形传递函数解法。该方法将矩形板在一个方向上离散为多个条形单元,而条形单元状态变量的解在单元的横向采用多项式插值,在单元的纵向直接解析求解。通过定义结点变量,并利用结点位移连续和力平衡条件,将多个简单子区域的解进行组装,可构造出分析复杂形状、复杂边界条件中厚板的条形传递函数解。数值算例表明,条形传递函数方法具有很高的计算精度。

Based on the Mindlin plate theory and modified mixed variational principle, the strip distributed transfer function method (SDTFM) with mixed state vector is proposed for the analysis of rectangular moderately thick plates. In this method, a plate is divided into a number of strip elements. In the lateral direction, the responses of the strip elements are interpolated by polynomials in terms of unknown nodal line state vector, and the nodal line state vector along the strip longitudinal direction is given in the analytical colsed-from. Introducing the nodal displacement vector and enforcing displacement continuity and force equilibrium at the inter-connecting nodes, the different rectangular substructures are assembled to give the solutions of moderately thick plates with complex geometric configurations and arbitrary boundary conditions. Numerical examples are provided to show the efficiency and high accuracy of the strip distributed transfer function method.