Integration of Spatial Nonlinear Beam Elements in Large Displacement Analysis: Theory and Applications

A consistent increase in the computational power over the past few decades has facilitated the integration of high-fidelity flexible multibody systems (MBS) framework and the finite element (FE) method into the engineering product design process. The choice of FE formulation plays a crucial role in determining the robustness, efficiency and accuracy of an MBS differential-algebraic equations solver. The flexible bodies in an MBS model can be characterized by either small deformation or large deformation. In either of the cases, handling the nonlinearities arising from reference-motion finite rotations becomes of key importance and challenging in order to have algorithms that can integrate finite elements in the non-incremental MBS solution procedures in a robust manner. Therefore, it is important to develop such formulations and evaluate their performance for different applications. This thesis is aimed at introducing new spatial beam finite elements based on the non-incremental formulations, the absolute nodal coordinate formulation (ANCF) and the consistent rotation-based formulation (CRBF). Furthermore, the spatial beam elements will be used to study several high-fidelity applications. The primary objectives of this thesis are threefold, which are summarized below. As one of the goals of this thesis, the CRBF is used to develop new three-dimensional beam elements starting with the ANCF kinematic description. While the proposed elements employ orientation parameters as nodal coordinates, independent rotation interpolation is avoided, leading to unique displacement and rotation fields. Furthermore, the proposed spatial ANCF/CRBF-based beam elements adhere to the non-commutative nature of the rotation parameters, allow for arbitrarily large three-dimensional rotation, and eliminate the need for using co-rotational or incremental solution procedures. Because the proposed elements have a general geometric description consistent with computational geometry methods, accurate definitions of the shear and bending deformations can be developed and evaluated, and curved structures and complex geometries can be systematically modeled. Three new spatial ANCF/CRBF beam elements, which use absolute positions and rotation parameters as nodal coordinates, are proposed. The time derivatives of the ANCF transverse position vector gradients at the nodes are expressed in terms of the time derivatives of rotation parameters using a nonlinear velocity transformation matrix. The velocity transformation leads to lower-dimensional elements that ensure the continuity of stresses and rotations at the element nodal points. The numerical results obtained from the proposed ANCF/CRBF elements are compared with the more general ANCF beam elements and with elements implemented in a commercial FE software. This objective of the thesis particularly sheds a light on the theoretical aspects of beams FE’s. The following two objectives of this thesis are focused on the study of beam elements for different MBS and FE applications. In the first objective of the two applications studied in this thesis, the computational MBS algorithms are used to develop detailed railroad vehicle models for the prediction of the wear resulting from the pantograph/catenary dynamic interaction. The wear is predicted using MBS algorithms for different motion scenarios that include constant-speed curve negotiation, and acceleration and deceleration on a tangent (straight) track. The effect of the vehicle vibration in these different motion scenarios on the contact force is further used to study the wear rates of the contact wire. The wear model used in this thesis accounts for the electrical and the mechanical effects. The nonlinear finite element ANCF, which is suitable for implementation in MBS algorithms, is used to model the flexible catenary system, thereby eliminating the need for using incremental rotation procedures and co-simulation techniques. In order to obtain efficient solutions, the overhead contact line and the messenger wire, both are modeled using the gradient deficient ANCF cable element. The pantograph/catenary elastic contact formulation employed in this thesis allows for separation between the pantograph pan-head and the contact wire, and accounts for the effect of friction due to the sliding between the pantograph pan-head and the catenary cable. The approach proposed in this thesis can be used to evaluate the electrical contact resistance, contribution of the arcing resulting from the pan-head/catenary separation, mechanical and electrical wear contributions, and effect of the pantograph mechanism uplift force on the wear rate. Numerical results are presented and analyzed to examine the wear rates for different motion scenarios. In the final objective of this thesis, FE structural dynamics algorithms are used along with MBS techniques to develop detailed railroad track substructure models to analyze the differential settlement in the ballast due to dynamic cyclic loading conditions. A cap plasticity material model is used in order to capture the geotechnical behavior of the ballast. The cap plasticity model includes enhancements to the Sandia GeoModel, such as improved computational tractability, robustness and domain of applicability. The material properties needed for the plasticity GeoModel are characterized with the help of several experimental triaxial compression tests on rail ballast. The ballast is divided into elastic and plastic regions to represent areas where the railway track is more prone to differential settlement, such as the ends of tunnels or passages over culverts. The rails are modeled using ANCF gradient-deficient beam elements, allowing seamless integration of beams with nonlinear structural dynamics algorithms and simplifying the procedure to update the geometry while running simulations with the MBS code. The solver to numerically integrate of the second order differential equations of motion is implemented in an in-house code. MBS algorithms are used to extract wheel-rail contact forces. Numerical results are presented and analyzed in the presence and absence of inelasticity considerations for the ballast.