Multidirectional displacement control algorithm

In seismically active regions, accuracy in predicting the behavior of buildings with reinforced concrete walls is crucial. The demand for reliable simulations has driven the development of two nonlinear analysis approaches: force-controlled and displacement-controlled. Traditional force-controlled iterative algorithms, when faced with complex nonlinear load-displacement patterns, often have convergence problems, especially near critical points such as post-peak instabilities or during the softening phase of the response. In such cases, the use of the unidirectional displacement control algorithm proposed by Batoz and Dhatt (1979) has proven to be more effective. However, the need to understand the behavior of structural walls with irregular cross sections has increased experimental studies on this type of specimen subjected to multidirectional cyclic loads, especially in countries such as Spain, Switzerland, Germany, and Japan. Despite the efforts, reproducing such complex behaviors in numerical models is still a challenge with the algorithms currently available, which is why this work introduces a new formulation and convergence strategy that extends the traditional unidirectional displacement control algorithm to a multidirectional approach. The key innovation of this work lies in its ability to perform simultaneous displacement control over multiple degrees of freedom, enabling accurate nonlinear analysis of more complex demand patterns. The proposed algorithm provides a robust solution for simulating advanced nonlinear behavior, addressing a significant gap in current numerical modeling practices. This extension has been rigorously validated by analyzing reinforced concrete walls with irregular cross-sections, demonstrating its superior performance under multidirectional loading.