Finite Element Formulation For Analysis Research Articles

Finite-Element Formulation for Analysis of Laminated Composites

This paper presents a multilayered/multidirector and shear-deformable finite-element formulation of shells for the analysis of composite laminates. The displacement field is assumed continuous across the finite-element layers through the composite thickness. The rotation field is, however, layerwise continuous and is assumed discontinuous across these layers. This kinematic hypothesis results in independent shear deformation of the director associated with each individual layer and thus allows the warping of the composite cross section. The resulting through-thickness strain field is therefore discontinuous across the different material sets. Numerical results are presented to show the performance of the method.

A computational method for design sensitivty analysis of elastoplastic structures

Design sensitivity analysis of structural systems having elastoplastic material behavior is developed using the continuum formulation and its implementation into a finite element program is described. The main idea is to develop a computational procedure for design sensitivity analysis based on the response obtained by an incremental load approach for non-linear response analysis, where the elastoplatic (time-independent) constitutive model is employed to account for the plastic material behavior; i.e. kinematic hardening and isotropic hardening. Discontinuities in the design sensitivity coefficients are investigated and a procedure is proposed to alleviate them. The control/reference domain approach is used to treat shape and non-shape design variables simultaneously. The direct variation method is adopted for this path-dependent problem to obtain the design sensitivity expression for the response variables. Analytical examples are used to demonstrate the developed sensitivity procedure and gain insights for numerical implementation. The design sensitivity expression is discretized to implement it into a computer program using the isoparametric formulation of finite element analysis. Numerical examples are presented to calculate the design sensitivity coefficients and compare them with those using the central finite difference method.

A temperature‐based formulation for finite element analysis of generalized phase‐change problems

AbstractA finite element formulation for solving multidimensional phase‐change problems is presented. The formulation considers the temperature as the unique state variable, it is conservative in the weak form sense and it preserves the moving interface condition. In this work, an approximate jacobian matrix that preserves numerical convergence and stability is also derived. Furthermore, a comparative analysis with other different phase‐change finite element techniques is performed. Finally, several numerical examples are analysed in order to show the performance of the proposed methodology.

A finite strain, total Lagrangian finite element solution for metal extrusion problems

A detailed formulation for finite element analysis of metal forming problems is carried out in this work. It incorporates every aspect of the analysis, including the iterative solution procedures for geometric and material non-linearities, implementation of the material model, and formulation of curved contact surfaces. The finite element formulation is based on a total Lagrangian approach which by-passes the use of the Jaumann stress rate tensor commonly used in the updated Lagrangian formulation. The yield model used is of the Von Mises type with both kinematic and isotropic hardening and is formulated in the Eulerian space. This model is then transformed to the Lagrangian reference frame. Stresses and the plastic strain components are evaluated using an elastic predictor-radial corrector algorithm with subincrementation. The curved contact boundaries are modeled using Hermite parametric curves, although other formulations such as β-splines and Bésier parametric curves may also be used with slight modifications. Applicability of these formulations in solving extrusion problems is examined through several runs performed using the UNIFES program developed by the authors. It is shown how the distance between the nodes on the die interface can lead to fluctuations in the extrusion pressure and how the amplitude of these fluctuations may be reduced by mesh refinement. A detailed account of the solution procedures is also provided.

Mixed formulations for finite element analysis of magnetostatic and electrostatic problems

This paper presents some mixed formulations for finite element analysis of magnetostatic and electrostatic problems. We employ the magnetic and electric fields as fundamental unknowns instead of the vector potential and the scalar potential, and the proposed approach appears to be desirable for three-dimensional finite element analyses. We also give brief comments on the use of the vector potential for the magnetostatic problem.

Mixed and penalty formulations for finite element analysis of an eigenvalue problem in electromagnetism

In this paper, we will present some weak formulations (variational formulations) for an eigenvalue problem in electromagnetism. In particular, mixed and penalty formulations are discussed, and some numerical results based on the mixed finite element method are given.

A finite element scheme for attenuation in ducts lined with porous material: Comparison with experiment

A general finite element formulation for analysis of the sound field in a uniform flow duct with a bulk-reacting porous liner is given. Numerical results on rectangular ducts lined on all four sides are shown, and some of the lower order acoustic modes are described. Comparison is made between numerically predicted and measured values of modal axial attenuation rate, phase speed and transverse pressure profile both with and without mean airflow. Generally good agreement between prediction and measurement is observed.

Lagrange-type formulation for finite element analysis of non-linear beam vibrations

A Lagrange-type formulation for finite element analysis of non-linear vibrations of immovably supported beams is presented. Two equations of motion coupled in axial and transverse displacements are derived by using Lagrange's equations. By neglecting the in-plane inertial effects, these equations are written in terms of the transverse displacement alone. Upon defining certain properties for the non-linear oscillatory behaviour of the transverse displacement, the governing equation is reduced to an equation in space alone from which the eigenvalue-like quantity is computed. The governing equation is solved in two ways. A direct iteration technique is used in the first method to compute a numerically exact mode shape and the corresponding frequency. A Rayleigh quotient type of formulation, similar to linear vibration analysis, is used in the second approach to evaluate the frequency of vibration for a fundamental mode which is determined from a linear FEM model and is maintained constant at all amplitudes. Numerical results are compared with available results and they corroborate the observations of earlier research workers.

A fast stiffness formulation for finite element analysis of two‐dimensional solids

AbstractThis paper describes and efficient method for computing two‐dimensional element stiffness matrices. It is a generalization of the algorithm given by Taylor. 1Theory is developed for elements which are loaded under plane stress, plane strain or axisymmetric conditions, and two FORTRAN IV subroutines are included. These subroutines, which are presented in a modular form, are applicable to any type of serendipity, Lagrangian or triangular element, and may be incorporated into a user's library. Alternatively, if desired, the relevant code may be embedded directly into existing stiffness generation routines.

Finite element formulation and solution of nonlinear heat transfer

A general and effective finite element formulation for analysis of nonlinear steady-state and transient heat transfer is presented. Heat conduction conditions, and convection and radiation boundary conditions are considered. The solutions of the incremental heat transfer equations is achieved using Newton-Raphson iteration, and in transient analysis using a one-step α-family time integration scheme. The stability and accuracy of the time integration is discussed. The solution techniques have been implemented, and the results of various sample solutions are discussed and evaluated.

A Finite Element Formulation for Analysis of Polycrystal Plasticity and General Discussion on Plasticity Theory

A Finite Element Formulation for Analysis of Polycrystal Plasticity and General Discussion on Plasticity Theory