Arc‐Center Arc‐Length Method for Non‐Linear Static Analysis of Curvilinear‐Fiber Laminated Plates

This paper proposes a simple and efficient arc‐length‐type method, called the Arc‐Center Arc‐Length Method (ACALM). Representative arc‐length formulations are briefly reviewed and compared to clarify its motivation and distinction. Based on the mathematical proof that a single equilibrium path is non‐self‐intersecting within the augmented state space, ACALM can provide theoretical guarantees for maintaining consistent forward search and avoiding tracing back. The implementation of ACALM is straightforward, based on only one set of computational formulas and two simple distance‐comparison criteria. In ACALM, the current arc‐length constraint center is located on the tangent line at the last equilibrium point, while making this point lie on the current arc‐length constraint surface. In this case, the intersection volume between current and previous arc‐length constraint domains provides crucial information to ensure forward search, which leads to the arc‐center selection criterion. The root selection criterion is presented with full Newton's method and few allowed iterations to capture the characteristics near turning regions with reasonable computational costs, through which the issue of complex roots is also avoided. Together with a recently proposed meshfree energy element method (EEM), ACALM is first applied to the non‐linear static analysis of complex‐shaped curvilinear‐fiber laminated plates (CFLP) with symmetric or unsymmetric layup configurations. Comparison of benchmark examples demonstrates the effectiveness, accuracy, and generality of the present solution.