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A force method version of three-dimensional Goodman joint elements
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DOI：10.1016/j.ijrmms.2026.106532.png)
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Abstract
En 中文
The analysis of discontinuous deformation caused by geological structural planes and artificial interfaces, hereafter collectively referred to as joints, is a tough challenge in geotechnical engineering. The Goodman joint element is the earliest yet still most widely used contact element due to its ease of implementation. However, under cyclic loading, the Goodman joint element exhibits very poor numerical characteristics, particularly manifested in poor convergence and non-physical oscillations of contact-related quantities. The situation is even worse for three-dimensional cases owing to the indeterminacy of the sliding direction. Considering that the Goodman joint element is implemented within the framework of displacement-based finite elements, and ill-posed problems in the displacement method can be easily transformed into well-posed ones in the force method framework, this study takes contact stress as the primal unknown quantity and directly applies it to both sides of the joint by releasing the constraints at the joint. Meanwhile, the unilateral constraints on displacement and contact stress at the joint are formulated as quasi-variational inequalities. Subsequently, drawing on the projection-contraction algorithm for standard variational inequalities and Gauss-Seidel iteration technique, the algorithm 3DFMVGE is designed, which is implemented through process iteration instead of state iteration. The proposed procedure strictly satisfies the contact conditions and avoids the introduction of artificial springs in the Goodman joint element. Both standard benchmark examples and engineering cases consistently demonstrate that the numerical characteristics of 3DFMVGE are far superior to those commonly used methods such as master-slave procedure.
Keywords:
Force method
Goodman joint element
Contact mechanics
Three-dimensional analysis
Variational inequalities
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