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Article Dans Une Revue Computer Methods in Applied Mechanics and Engineering Année : 2022

Partitioned path-following strategy for nonlinear structural analyses using the boundary element method

Résumé

The appearance of snapping phenomena is frequent in structural analyses involving nonlinearities such as the propagation of localized damage zones, or cracks, as encountered in quasi-brittle materials. In the presence of snapping effects, the standard Newton-based algorithms cannot predict the equilibrium curves correctly by usual displacement or force control. This problem can be circumvented by using path-following techniques. This study proposes a numerical approach for nonlinear structural analysis based on the Boundary Element Method (BEM) coupled with a partitioned path-following strategy. In this strategy, the acting loads are divided into two groups: (a) those perfectly known and (b) those in which only the direction is known, while the magnitude (or load factor/multiplier) is determined to respect the equilibrium of the boundary fields (indirectly controlled) and an additional problem equation, the path-following constraint equation. The resulting nonlinear system is solved using an incremental iterative scheme. For each iteration, the corrections to the boundary fields are obtained in a partitioned manner. First, the portion coming from the unbalanced boundary fields is calculated. Then the correction resulting from a unit load in the direction of the load to be indirectly controlled is obtained. Finally, the load factor is calculated independently using the path-following constraint equation, which can be linear, nonlinear, differentiable, or not. In the numerical tests, the Control of the Nodal Displacement Increment (CNDI) is chosen as path-following constraint equation for the sake of illustration. The results show that the proposed approach can efficiently capture the equilibrium curve even in the presence of severe snap-backs. The approach is designed to be implemented in existing BEM codes straightforwardly, provided that the influence matrices can be accessed. Moreover, no additional pre-conditioning technique is required.
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Dates et versions

hal-04019583 , version 1 (08-03-2023)

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Hugo Luiz Oliveira, Giuseppe Rastiello, Alain Millard. Partitioned path-following strategy for nonlinear structural analyses using the boundary element method. Computer Methods in Applied Mechanics and Engineering, 2022, 394, pp.114875. ⟨10.1016/j.cma.2022.114875⟩. ⟨hal-04019583⟩
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