|M.Sc Student||Pestes Yehonatan|
|Subject||Development of a Cosserat Point Element for Non-Linear|
|Department||Department of Civil and Environmental Engineering||Supervisor||Professor Mahmood Jabareen|
|Full Thesis text - in Hebrew|
Numerical methods are a common tool in solving complex engineering problems in structural dynamics, where the most popular one is the Finite Elements Method. It is well known that the standard displacement formulation suffers from numerous shortcomings, including volumetric locking when modeling nearly incompressible materials, inability to describe the bending of thin structures, sensitivity to irregular mesh shapes, and inaccuracy when using coarse meshes. Recently, a promising new formulation was developed, denoted as the Cosserat Point Element (CPE). This finite element (FE) formulation predicted impressive results in simulating the static behavior of benchmark problems while overcoming the above-mentioned shortcomings. Thanks to the novel kinematic measures and splitting the deformation into homogenous and inhomogeneous parts, the CPE exhibits excellent robustness. Also, due to the average kinematic quantities, the kinetic quantities were defined by differentiation of the strain energy function rather than integration, which led to enhancing the computational efficiency of the element.
In order to numerically solve dynamic problems using the FE method, time integration methods are required. As documented, most time integration methods - when used in linear analyses - are unconditionally stable, i.e. they can predict accurate responses providing an appropriate finite element formulation is chosen. In non-linear dynamic problems, however, such time integration schemes may become unstable, and thus finite element formulation may predict inaccurate results.
In this study, time integration schemes of implicit and explicit methods are implemented with the CPE in order to solve non-linear dynamic problems. Accordingly, this study is divided into two main parts. The first part deals with implicit methods, where a calculation procedure was developed using the methods of HHT-α, WBZ-α, Generalized-α, and the Generalized Energy Momentum Method (GEMM). The results obtained from using these methods along with the CPE were examined, leading to the conclusion that the GEMM provided the most stable and accurate solutions. Furthermore, predictions carried out by the HTT-α method along with the CPE were compared with those obtained by two other FE formulations that are available in the commercial FE package (ABAQUS). The first formulation is based on the reduced integration with hourglass control (C3D8R), while the second is based on the enhanced strain method (C3D8I). It was found that CPE formulation led to accurate and stable results while the other formulations failed to manage that. The second part of the study deals with explicit methods, where the performance of the CPE used along with the central difference method is compared with those obtained from the C3D8R and C3D8I. It was concluded here that the performance of the C3D8R and C3D8I formulations was influenced by unphysical damping that caused inaccurate results while the CPE managed to predict the accurate response of the structure.
In conclusion, this study showed that the CPE implemented along with implicit and explicit methods serves as an accurate, reliable and stable tool for solving complex engineering problems. In addition, the CPE is capable of accurately solving non-linear dynamic problems while other formulations (C3D8I, C3D8R) showed difficulties in obtaining accurate and stable solutions.