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选用更具广泛性的横观各向同性弹性半空间地基模型,来分析四边自由各向异性矩形地基板的弯曲解析解.将异性薄板的弯曲控制方程,与基于横观各向同性弹性半空间地基位移解建立的板与地基变形协调方程相结合,先按对称性分解,然后用三角级数法,得出横观各向同性弹性半空间地基上四边自由各向异性矩形薄板的弯曲解析解,包括地基反力、板的挠度及内力的解析表达式.该解析解克服了数值法的弊端,取消了对地基反力的假设,板的内力及地基反力求解更切实际.算例结果与文献结果吻合良好,证明本文方法的可行性.
A more generalized isotropic elastic half-space foundation model is chosen to analyze the analytical solution of the bending of free-form anisotropic rectangular foundation on four sides. The bending control equation of the opposite-shaped sheet is compared with that based on the transversely isotropic elastic half-space Combined with the foundation deformation deformation coordination equation, the foundation plate displacement-deformation coordination equation is firstly decomposed by symmetry and then by the trigonometric series method, the bending analytical solution of the free-form anisotropic rectangular plate on the transversely isotropic elastic half space foundation is obtained Including analytic expressions of foundation reaction force, plate deflection and internal force.The analytical solution overcomes the drawbacks of the numerical method and cancels the hypothesis of the foundation reaction force, and the internal force of the plate and the foundation reaction force are more realistic. The results are in good agreement with the literature to prove the feasibility of this method.