This paper shows the development of a displacement potential function based on the Galerkin potential using complex variables. The displacement potential function results in a more suitable method for numerical calculations since it avoids the strenuous integration process associated with stress potential methods. Completeness of the displacement potential function is demonstrated. The displacement potential function was applied to the solution of the first fundamental problem of elasticity over a three-dimensional domain with known boundary conditions. It’s application for numerical calculations is demonstrated by solving the pure shear problem over a three-dimensional unit hexahedral cell. Finally, the obtained numerical results are compared against finite element results, proving the validity of the displacement potential function in solving three-dimensional linear elasticity problems.

本文展示了使用复杂变量基于Galerkin势的位移势函数的开发。由于位移势函数避免了与应力势方法相关的费力的积分过程，因此它导致了一种更合适的数值计算方法。证明了位移势函数的完整性。将位移势函数应用于已知边界条件的三维域上的第一个基本弹性问题的解决方案。通过求解三维单位六面体单元上的纯剪力问题，证明了其在数值计算中的应用。最后，将获得的数值结果与有限元结果进行比较，