四种非正交边界板考虑初始荷载效应的后期荷载位移近似解

基于考虑初始荷载效应情况下板的一般形式的静力平衡微分方程，运用坐标变换得到了轴对称情形，考虑初始荷载效应后圆形板的极坐标形式的静力平衡微分方程。运用Galerkin法解得了简支等边三角形板、固支椭圆板、固支圆形板和简支圆形板四种非正交边界板考虑初始荷载效应的后期荷载位移近似解。运用相关文献提出的有限元法验证了近似解的正确性。各位移近似解表达式简单、物理意义明确，清楚地反映了初始荷载及相关因素对后期荷载位移的影响。计算分析表明：初始荷载效应提高了板的弯曲刚度，减小了板的后期荷载位移；板的初始荷载效应主要受初始荷载、跨厚比及边界条件等因素的影响。

Later Load Displacement Approximate Solution Under Initial Loads for Four Non-orthogonal Boundary Plates

Based on general static equilibrium differential equation of plate considered initial load effect, the polar form static equilibrium differential equation was presented for circular plate considered initial load effect under axisymmetric condition. The approximate solutions of later load displacement considered initial load effect for the simply supported equilateral triangular plate, the clamped ellipse plate, the clamped circular plate and the simply supported circular plate, were derived by the Galerkin method. These approximate solutions of displacement were verified using the finite element method presented in related literature. Initial load effect on later load displacement of the above 4 plates was analyzed with these solutions, which clearly illustrated the initial load effect and corresponding factors that influence the static performance of plates. Due to initial loads effect, the bending stiffness of plate increased, the displacements of later loads decreased. The key physical factors governing the effect of initial loads on plates are the initial load, the ration of span to thickness and boundary condition etc.