A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures
| Autor: | H. A. Santos, José Paulo Moitinho de Almeida, Paulo de Mattos Pimenta |
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| Rok vydání: | 2011 |
| Předmět: |
Discretization
Differential equation Applied Mathematics Mechanical Engineering Mathematical analysis Linear elasticity Computational Mechanics Ocean Engineering Mixed finite element method Rigid body Finite element method Computational Mathematics symbols.namesake Computational Theory and Mathematics Lagrange multiplier symbols Boundary value problem Mathematics |
| Zdroj: | Computational Mechanics. 48:591-613 |
| ISSN: | 1432-0924 0178-7675 |
| DOI: | 10.1007/s00466-011-0608-3 |
| Popis: | This paper addresses the development of a hybrid-mixed finite element formulation for the quasi-static geometrically exact analysis of three-dimensional framed structures with linear elastic behavior. The formulation is based on a modified principle of stationary total complementary energy, involving, as independent variables, the generalized vectors of stress-resultants and displacements and, in addition, a set of Lagrange multipliers defined on the element boundaries. The finite element discretization scheme adopted within the framework of the proposed formulation leads to numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the equilibrium boundary conditions. This formulation consists, therefore, in a true equilibrium formulation for large displacements and rotations in space. Furthermore, this formulation is objective, as it ensures invariance of the strain measures under superposed rigid body rotations, and is not affected by the so-called shear-locking phenomenon. Also, the proposed formulation produces numerical solutions which are independent of the path of deformation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions compared with those obtained using the standard two-node displacement/ rotation-based formulation. |
| Databáze: | OpenAIRE |
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