A numerical approach for equilibrium and stability analysis of slender arches and rings under contact constraints (original) (raw)
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Optimization Techniques Applied to Structural Unilateral Contact Problems
2005
Structural elements are sometimes supported by other bodies that may offer resistance only in certain directions. Problems where the structure can get or lose contact with other bodies, or even slide on its support, are usually found in the literature with the denomination of unilateral contact problems. In this work two alternative methodologies are proposed for the solution of unilateral
Stability of arches and beams under unilateral constraints
A numerical methodology is presented in this paper for the budding and post-buckling analysis of slender structural elements such as arches and beams subjected to unilateral contact constraints. A geometrically non-linear finite element model is used together with an updated Lagrangian formulation to obtained the non-linear equilibrium paths for perfect and imperfect structural models. The unilateral constraints are imposed by tensionless elastic or rigid foundations. At each load step, in order to obtain the equilibrium configuration and contact regions, the equilibrium equations are linearized and the contact problem is treated as a minimization problem with inequality constraints. The resulting linear programming problem is solved by the use of Lemke's algorithm and the contact regions are identified. Next, the Newton-Raphson method is used with path following methods to obtain the new contact forces and equilibrium configurations. Some structural systems are analyzed and the computational results show that the proposed methodology is feasible and efficient and that the results compare well with experimental and other numerical results found in literature.
A nonlinear modal solution methodology capable of solving equilibrium and stability problems of structural systems (beams and arches) with contact constraints is presented in this work. The contact constraints are imposed by elastic foundations of the Winkler type, where special attention is given to the case in which the foundation reacts in compression only. characterizing the contact as unilateral. A Ritz type approach with moveable boundaries is proposed to solve this class of unilateral contact problems. The proposed methodology is illustrated by particular problems involving beam-columns and arches, and the results are compared with available results obtained by finite element and mathematical programming techniques.
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