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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.采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.
Based on the static equilibrium differential equation of the general form of the plate considering the initial loading effect, the axial symmetry is obtained by coordinate transformation, and the static equilibrium differential equation in the polar form of the circular plate is taken into account after the initial loading effect. By using the Galerkin method The approximate solution of late loading displacement considering the initial load effect is obtained for four kinds of non-orthogonal boundary plates, such as simply supported equilateral triangular plate, fixedly supported elliptical plate, solid circular plate and simple circular plate. Finite element method proposed by relevant literature The correctness of the approximate solution is validated.The expressions of approximate solution of each displacement are simple and have clear physical meaning and clearly reflect the influence of initial load and related factors on late load displacement.The calculation and analysis show that the initial load effect improves the bending stiffness of the plate, Reduce the late load displacement plate; initial load effect of the plate is mainly affected by the initial load, cross-over ratio and boundary conditions and other factors.