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针对线性各向异性弹性体小变形接触问题,将弹性体按是否与刚体压头发生接触进行划分,基于Eshelby-Stroh公式求解各个部分的位移函数和应力函数,进一步通过应力函数积分得到载荷值。考虑到求解结果存在交接处应力突变和非接触区域应力不近似于零的问题,采用整体位移约束法和线性叠加原理,通过迭代方式使位移函数和应力函数逼近理想解,解决了圆柱压头和倒圆角楔形压头与弹性体的接触问题。基于圆柱压头求得的载荷值比R.C.Batre求解得到的结果更近于Hwu和Fan的弹性半空间法求解结果,当K=400时计算得到的相对误差仅为0.52%。基于圆柱压头和倒圆角楔形压头求得的载荷值与ABAQUS仿真结果较为吻合:圆柱压头载荷值的相对误差为0.67%;倒圆角楔形压头,对6个不同的圆角值进行计算,载荷的相对误差都小于2%。
Aiming at the small deformation contact problem of linear anisotropic elastic body, the elastic body is divided according to whether it is in contact with the rigid body pressure head. Based on the Eshelby-Stroh formula, the displacement function and stress function of each part are solved, and the load value is further integrated by stress function. Considering the problem of sudden change of stress and non-zero stress in the non-contact area, the displacement displacement function and stress function are approximated to the ideal solution by the iterative method by using the integral displacement constraint method and the linear superposition principle. Round wedge indenter and elastomer contact problems. The load value obtained by the cylinder head is more approximate than that obtained by R.Catre’s solution. The result of elastic half-space method by Hwu and Fan shows that the relative error is only 0.52% when K = 400. The load values obtained by the cylindrical head and the round wedge head are in good agreement with the ABAQUS simulation results. The relative error of the load on the cylinder head is 0.67%. For the rounding wedge head, Calculated, the relative error of the load is less than 2%.