Parallelized Element-By-Element Solver for Structural Analysis of Flexible Pipes Using Finite Macroelements

Abstract

Due to the number of layers and their respective geometrical complexities, finite element analyses of flexible pipes usually require large-scale schemes with a high number of elements and degrees-of-freedom. If proper precautions are not taken, such as suitable algorithms and numerical methods, the computational costs of these analyses may become unfeasible. Finite macroelements are finite elements formulated for the solution of a specific problem considering and taking advantage of its particularities, such as geometry patterns, to obtain computational advantages, as reduced number of degrees-of-freedom and ease of problem description. The element-by-element (EBE) method also fits very well in this context, since it is characterized by the elimination of the global stiffness matrix and its memory consumption grows linearly with the number of elements, besides being highly parallelizable. Over the last decades, several works regarding the EBE method were published in the literature, but none of them directly applied to flexible pipes. Due to the contact elements between the layers, problems with flexible pipes are usually characterized by very large matrix bandwidth, making the implementation of the EBE method more challenging, so that its efficiency and scalability are not compromised. Therefore, this work presents a parallelized implementation of an element-by-element architecture for structural analysis of flexible pipes using finite macroelements. Four synchronization algorithms were developed and analyzed in detail, including their scalability assessment, and comparisons were made with a well-established finite element method (FEM) software with significant gains in simulation time and memory consumption.