本文将非线性的接触问题线性化 ,即假设已知带可调参数的接触区载荷分布模态以及接触区宽度 ,再反求圆柱压头的半径。首先根据叠加原理将受力状态分解成对称和反对称状态 ,然后用正交完备的三角级数和勒让德级数构造这两种受力状态的位移场 ,并应用最小势能原理确定位移场中的待定系数 ,从而确定层合梁的位移场和应力场。载荷分布模态中的可调参数可根据接触区表面的位移协调条件确定 ,从而求得圆柱压头的半径。最后 ,由于在给定接触区的条件下压头曲率与压头合力成正比 ,故可以得到压头曲率在不同的接触区下随载荷变化的直线族。根据这些直线族 ,可以由已知的压头曲率和外载荷确定接触区尺寸。计算结果显示 ,这种解法的收敛性非常好。根据物理方程与根据平衡方程得到的层合梁剪应力分布的一致性非常好。而且 ,在远离接触区处的应力分布同经典层合梁理论结果的一致性也非常好 In this paper, the non-linear contact problem is linearized, that is, it is assumed that the contact zone load distribution model with adjustable parameters and the contact zone width are known, and the radius of the cylinder head is inversely determined. Firstly, the stress state is decomposed into symmetrical and antisymmetric states according to the principle of superposition, and then the displacement fields of these two stress states are constructed by orthogonal complete triangular series and Legendre series, and the displacement field is determined by the principle of minimum potential energy In the undetermined coefficient, to determine the displacement of the laminated beam and stress field. The adjustable parameters in the load distribution modal can be determined according to the displacement coordination condition on the surface of the contact zone so as to obtain the radius of the cylinder head. Finally, since the indenter curvature is proportional to the resultant force of the indenter at a given contact zone, a straight line family with varying indenter curvature over load can be obtained. From these linear families, the contact zone size can be determined from the known head curvature and external load. The calculation results show that the convergence of this solution is very good. The consistency of the shear stress distribution of the laminated beams according to the physical equation and the equilibrium equation is very good. Moreover, the distribution of stresses away from the contact zone is also very consistent with the theoretical results of classical laminated beams