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This paper presents a finite element formulation for the analysis of two dimensional reinforced elastic solids developing both small and large deformations without increasing the number of degrees of freedom. Fibers are spread inside the domain without the necessity of node coincidence. Contact stress analysis is carried out for both straight and c...
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Citations
... The geometric nonlinear behavior is modeled herein using the approach of Paccola et al. (2015). This formulation is known as positional finite element method (Positional FEM), which differs from the standard FEM in terms of the nodal parameters accounted in the system of equations. ...
Topology optimization is an effective approach for the efficient layout design of structures and their components. This approach is well-established in the solid mechanics’ domain for linear elastic and small-displacement conditions. However, the topology optimization of elastic structures under large-displacement conditions has been marginally addressed in the literature. This study proposes a numerical formulation for the topology optimization analysis of plane structures subjected to geometrically nonlinear behavior. This formulation couples positional finite elements to the solid isotropic material with penalization method. High order positional finite elements have been utilized, which enable high accuracy on the mechanical fields’ assessment. The proposed formulation achieves the benchmark responses available in the literature for geometric linear conditions, as expected. Nevertheless, the topology optimization analysis accounting for geometric nonlinear conditions leads to final geometries largely different from those predicted in linear conditions. Two applications demonstrate the accuracy of the proposed numerical scheme and emphasize the importance of handling properly the geometric nonlinear effects into real engineering design.
In this study, for the first time, we present a shell finite element based on positions and generalized vectors for instability analysis of thin-walled members. The presence of generalized vectors and transverse strain enhancement guarantee to the proposed formulation a good representation of strain and stress fields inside the element, allowing the use of complete three-dimensional constitutive law without any locking. The proposed formulation is total Lagrangian and naturally covers large displacement modeling. In past studies, the presence of generalized vectors limited the connection of shell portions or non-tangential panels, making it difficult to model thin-walled members. To solve this problem, a strategy to ensure the connection between non-coplanar elements, considering the stiffness of the connecting material, is originally developed and presented in this paper.
In numerical examples we explore differences among buckling load achieved using small displacements and first limit points (or bifurcation points) using large displacements. The influence and the sensitivity of the connection stiffness are also tested when comparing these values. Results are validated against literature reference values and new examples are proposed to show the applicability of the positional formulation.
This study intends to contribute with the improvement of FEM formulations to analyze composite materials and structures at the meso and macro levels. Specifically, composite materials and structures constituted by an elastic matrix reinforced by long or short fibers that may debound when the contact stress reaches a critical value are taken into account.
The study proposes a way to introduce fibers (short or long) inside elastic solids modeled by finite elements without increasing the number of degrees of freedom when debounding is not present. When there is debounding, new degrees of freedom are incorporated only at the slipping contact between fibers and matrix following an elastoplastic non-linear constitutive relation. The matrix is considered elastic while fibers follow a multi-linear elastoplastic constitutive relation. Large deformations and moderate strains are considered. In order to model the debounding between fibers and matrix it is necessary to accurately calculate the contact stresses. Therefore, the development of straight and curved fiber elements of any order and the accuracy analysis of the proposed contact stress calculations are investigated. After defining the best strategy to be followed general examples are solved to validate the contact stress calculation, debounding and plastic fiber behavior.
