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运用能量变分原理,给出了同时考虑初始纵、横向荷载效应情况下板的应变能表达和静力平衡微分方程;推导了同时考虑初始纵、横向荷载效应的板单元刚度矩阵.运用Galerkin法求解了同时考虑初始纵、横向荷载效应情况下3种典型板(固支矩形板、固支和简支圆形板)的后期横向荷载位移近似解.验证了考虑初始纵、横向荷载效应的板单元刚度矩阵和3种典型板的后期荷载位移近似解的正确性,并分析了初始纵、横向荷载效应对板的后期横向荷载位移的影响.结果表明:初始纵、横向荷载效应改变了板的弯曲刚度,将影响板承受后期横向荷载的静力性能;同时考虑初始纵、横向荷载效应情况下,板的静力性能主要受初始纵向和横向荷载、板的厚度及边界条件等因素的影响.
Using the principle of energy variation, the strain energy expression and static equilibrium differential equation of the plate under the consideration of the initial longitudinal and transverse load effects are given. The stiffness matrix of the plate element considering the initial longitudinal and transverse load effects is deduced. By using the Galerkin method The approximate solutions of late transverse load displacements of three kinds of typical plates (fixed rectangular plate, fixed circular plate and simple circular plate) considering the initial longitudinal and transverse load effects are also obtained. The plate considering the initial longitudinal and transverse load effects Element stiffness matrix and three kinds of typical plates, and analyzed the influence of the initial longitudinal and transverse load effects on the laterally lateral load displacement of the plate.The results show that the initial longitudinal and transverse load effects change the influence of the plate The bending stiffness will affect the static performance of the slab under the late transverse load. Meanwhile, considering the initial longitudinal and lateral load effects, the static performance of the slab is mainly affected by the initial longitudinal and transverse loads, the thickness of the slab and the boundary conditions.