半解析数值法分析四边自由中厚板的受力特性

根据Reissner中厚板理论,结合胡海昌的解耦函数法,本文构造出一种能满足全部自由边界条件的试函数,并以此建立两个广义位移,用该位移求得双参数地基上四边自由矩形中厚板弯曲问题的解析解.利用最小平方误差法并结合数值算例,重点探讨了板弯剪刚度比、地基刚度以及地基剪切模量对弹性地基上四边自由中厚板受力特性影响规律.结果显示:(1)Vlazov地基模型优于Winkle地基模型,因为它考虑了地基剪切刚度的影响,使得板的内力和挠度均有减小,发挥了地基的潜力;(2)当地基刚度较小时,地基的剪切模量对板的挠度和内力的影响显著;当地基的刚度较大时,剪切模量对板的内力和挠度的影响不明显.本文计算精度高,计算工作量小且便于对参数进行分析,以及提供数值分析法判据等多项特点.

Semi-Analytical Numerical Method for Analyzing Strength Characteristic of the Four Free Edge Moderate Thick Plate

According to Reissner's moderate thick plate theory and Hu Hai-chang's decoupling function method,the trial function that satisfied all and every free boundary conditions was established,two generalized displacements were determined,and the analytic solution of buckling problem of moderate thick plate with four free boundaries in two-parameter elastic foundation was obtained.Using least square error method and combining with the numerical example,the influence of ratio between flexural and shear rigidity,foundation stiffness and foundation shear module on moderate thick plate with four free boundaries in elastic foundation was analyzed.The analysis indicated that:(1) the Vlazov's foundation model was better than Winkler foundation model because it took into account the influence of foundation shear rigidity,thus reducing the internal force and deflection of plate and taking advantage of the foundation potential;(2) when the foundation stiffness was small,the foundation shear module had distinct influence on the internal force and deflection of the plate;when the foundation stiffness was large,the influence was not obvious.In addition,the method had high accuracy,little workload and was convenient for parametric analysis.