Search results for "Mixed finite element"
showing 10 items of 25 documents
A four-node MITC finite element for magneto-electro-elastic multilayered plates
2013
An isoparametric four-node finite element for multilayered magneto-electro-elastic plates analysis is presented. It is based on an equivalent single-layer model, which assumes the first order shear deformation theory and quasi-static behavior for the electric and magnetic fields. First, the electro-magnetic state of the plate is determined in terms of the mechanical primary variables, namely the generalized displacements, by solving the strong form of the magneto-electric governing equations coupled with the electro-magnetic interface continuity conditions and the external boundary conditions. In turn, this result is used into the layers constitutive law to infer the equivalent single-layer…
Finite Element Method Analysis of a Spur Gear with a Corrected Profile
2007
The difference between the stress value calculated by a two-dimensional finite element model of spur gears and those obtained by the rules in ISO 6336 was evaluated. Hertz theory, which provides information on the extension of the contact area and the maximum value of the contact pressure, was used to choose the dimensions of the elements. The mesh was created using the stress analytical solution relative to a model consisting of two cylinders in contact. Analogous optimization was executed for the mesh of the teeth feet; a mesh of 15 elements was considered optimum, because it minimized the difference to 0.5 per cent in the bending stress calculation. Stress values, obtained using the fin…
On finite element approximation of the gradient for solution of Poisson equation
1981
A nonconforming mixed finite element method is presented for approximation of ?w with Δw=f,w| r =0. Convergence of the order $$\left\| {\nabla w - u_h } \right\|_{0,\Omega } = \mathcal{O}(h^2 )$$ is proved, when linear finite elements are used. Only the standard regularity assumption on triangulations is needed.
A review on some discrete variational techniques for the approximation of essential boundary conditions
2022
We review different techniques to enforce essential boundary conditions, such as the (nonhomogeneous) Dirichlet boundary condition, within a discrete variational framework, and especially techniques that allow to account for them in a weak sense. Those are of special interest for discretizations such as geometrically unfitted finite elements or high order methods, for instance. Some of them remain primal, and add extra terms in the discrete weak form without adding a new unknown: this is the case of the boundary penalty and Nitsche techniques. Others are mixed, and involve a Lagrange multiplier with or without stabilization terms. For a simple setting, we detail the different associated for…
Finite element analysis in vertebrate palaeontology
2002
The Finite Element Analysis (FEA) is a numerical method which allows to analyse the static and dynamic behaviour of complex structures. A structure is substituted by a model consisting of a number of small, well-defined elements, each interconnected by nodes. Within the element attributes and material properties, the model can be exposed to static or dynamic loads. The displacements of the structure as the reaction to its loadings are calculated. Other data such as stress or strain at localized points in the structure are derived from these displacements. Originally developed for engineering, FEA soon was introduced to human medicine by modelling the behaviour of bone, teeth, cartilage and …
Parallel finite element splitting-up method for parabolic problems
1991
An efficient method for solving parabolic systems is presented. The proposed method is based on the splitting-up principle in which the problem is reduced to a series of independent 1D problems. This enables it to be used with parallel processors. We can solve multidimensional problems by applying only the 1D method and consequently avoid the difficulties in constructing a finite element space for multidimensional problems. The method is suitable for general domains as well as rectangular domains. Every 1D subproblem is solved by applying cubic B-splines. Several numerical examples are presented.
A smart composite-piezoelectric one-dimensional finite element model for vibration damping analysis
2015
A one-dimensional finite element method for generally layered smart beams is presented in this paper. The model implements the first-order shear deformation beam theory and is based on the preliminary analytical condensation of the electric state to the mechanical state. This allows us to establish an effective mechanical beam kinematically equivalent to the original smart beam including the effects of electro-elastic couplings. The contributions of the external electric loads are included in both the equivalent stiffness properties and the equivalent mechanical boundary conditions. Hermite shape functions, which depend on parameters representative of the staking sequence through the equiv…
Fast MATLAB assembly of FEM matrices in 2D and 3D: Edge elements
2014
We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in discretizations of H(div) spaces and Nedelec elements in discretizations of H(curl) spaces. We explain vectorization ideas and comment on a freely available MATLAB code which is fast and scalable with respect to time.
A beam finite element for magneto-electro-elastic multilayered composite structures
2012
Abstract A new finite element based upon an elastic equivalent single-layer model for shear deformable and straight magneto-electro-elastic generally laminated beam is presented. The element has six degrees of freedom represented by the displacement components and the cross-section rotation of its two nodes. The magneto-electric boundary conditions enter the discrete problem as work-equivalent forces and moments while the electro-magnetic state characterization constitutes a post-processing step. The element possesses the superconvergence property for the static problem of beams with uniform cross-section and homogenous material properties along the beam axis direction. Moreover, it is free…
The interphase finite element
2011
Mesomodelling of structures made of heterogeneous materials requires the introduction of mechanical models which are able to simulate the interactions between the adherents. Among these devices is quite popular the zero thickness interface (ZTI) model where the contact tractions and the displacement discontinuities are the primary static and kinematic variables. In some cases the joint response depends also on the internal stresses and strains within the thin layer adjacent to the joint interfaces. The interphase model, taking into account these additional variables, represents a sort of enhanced ZTI. In this paper a general theoretical formulation of the interphase model is reported and an…