Development of a Rotation Free Shell Element Capturing the Stretching and Bending of Thin Flexible Membranes Under Large Deformation and Large Strain Conditions
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Date
2018-01-01
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Department
Mechanical Engineering
Program
Engineering, Mechanical
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Access limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan thorugh a local library, pending author/copyright holder's permission.
This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
Abstract
Classical shell elements which contain nodal displacements and rotations as Degrees of Freedom (DOF) in structural analysis are difficult to use for applications involving solid-fluid interaction such as the red blood cells flowing in the blood stream in biomechanical analysis. Therefore, a nonlinear Rotation Free (RF) shell element dealing with the stretching and bending effects of thin membrane structures without directly involving nodal rotations as DOF needs to be developed. Such element can be incorporated in some analyses, like studying the movement and deformation of Red Blood Cells flowing in a prescribed blood stream. In this study, the Discrete Kirchhoff Triangular (DKT) shell and a triangular linear RF shell element based on Kirchhoff-Love plate theory are introduced and studied as needed to establish the foundation for the development of shell element with or without nodal rotations as DOF. Nonlinear finite element theory and nonlinear algorithms are employed establishing the framework for nonlinear finite element and algorithm development. Based on the above foundation, an advanced nonlinear RF shell element is proposed and developed using the Total Lagrangian method. The finite volume method is applied by taking the integral of the curvatures for implicit accounting of such element behavior, thus leading to the development of an RF non-linear shell element. Geometric and material nonlinearities are considered in formulating this element. This new element is developed in conjunction with the use of two nonlinear material models, i.e., the Neo-Hooken and Mooney-Rivlin materials which are often used in modeling biomaterial systems. The resulting nonlinear system of finite element equations is then solved using the incremental method in conjunction with the Newton Raphson method. This element is first formulated in a global system of reference for flat model analyses. Then, three local coordinate systems are established so that each element matrix could be properly calculated. With the aid of two transformation matrices and proper coordinate transformation from the local to the global system of reference, an updated nonlinear RF shell element is formulated for the model analyses in a Three Dimensional (3D) space. Relevant case studies aimed at validating this advanced nonlinear RF shell element under large deformation and large strain conditions are carried out. The results show that the newly developed element has high accuracy when compared to analytical solutions and the numerical results from the commercial package ABAQUS. It is expected that the development of this new non-linear, RF shell finite element will help advance the state-of-the-art in biomechanics as it relates to testing the efficacy of new drugs.