Multi-point support reaction forces calculation based on unilateral constraint

Preventing overturning of construction machinery necessitates precise calculation of support reaction forces. The primary challenges reside in: (1) statically indeterminate force distributions, (2) indeterminacy of ground-contact states at support points. While conventional engineering methods yield ambiguous solutions, finite element method (FEM) proves computationally intensive for this purpose. Crucially, the relationship between reaction force and penetration depth embodies a unilateral constraint mechanism. A method based on unilateral constraint that correlates micro-displacements of support structures with reaction forces is proposed in this study. By formulating equilibrium equations in terms of micro-displacements and providing initial values and the corresponding Jacobian matrix, the accuracy and computational efficiency are significantly enhanced. Several examples are provided to verify the correctness of the proposed method. The proposed method offers an innovative idea for resolving statically indeterminate problems while simultaneously determining contact states—a critical factor in construction machinery overturn analysis.