Showing papers on "Finite element limit analysis published in 2006"

A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries

Abstract: SUMMARY We present a Generalized Finite Element Method for the analysis of polycrystals with explicit treatment of grain boundaries. Grain boundaries and junctions, understood as loci of possible displacement discontinuity, are inserted into finite elements by exploiting the partition of unity property of finite element shape functions. Consequently, the finite element mesh does not need to conform to the polycrystal topology. The formulation is outlined and a numerical example is presented to demonstrate the potential and accuracy of the approach. The proposed methodology can also be used for branched and intersecting cohesive cracks, and comparisons are made to a related approach (Int. J. Numer. Meth. Engng. 2000; 48:1741). Copyright 2006 John Wiley & Sons, Ltd.

Homogenization approach for the limit analysis of out-of-plane loaded masonry walls

Abstract: This paper addresses the usage of a simplified homogenization technique for the analysis of masonry subjected to out-of-plane loading. The anisotropic failure surface, based on the definition of a polynomial representation of the stress tensor components in a finite number of subdomains, is combined with finite element triangular elements employed for the upper and lower bound limit analyses. Several comparisons between the proposed model and experimental data available in the literature are presented, for wallettes subjected to bending at different orientations and for different panels loaded out of plane. The limit analysis results allow us to identify the distribution of internal forces at critical sections and to obtain the collapse modes, as well as the failure loads. Excellent results are found in all cases, indicating that the proposed simple tool is adequate for the safety assessment of out-of-plane loaded masonry panels. The combined usage of upper and lower bound approaches, and their respective simplifications, allow us to define a narrow interval for the real collapse load.

Dynamics of Flexible Multibody Systems: Rigid Finite Element Method

Abstract: Homogenous Transformations.- The Rigid Finite Element Method.- Modification of the Rigid Finite Element Method.- Calculations for a Cantilever Beam and Methods of Integrating the Equations of Motion.- Verification of the Method.- Applications.

A Numerical Approach for Arbitrary Cracks in a Fluid-Saturated Medium

Abstract: A finite element method is proposed that can capture arbitrary discontinuities in a two-phase medium. The discontinuity is described in an exact manner by exploiting the partition-of-unity property of finite element shape functions. The fluid flow away from the discontinuity is modelled in a standard fashion using Darcy’s relation, while at the discontinuity a discrete analogon of Darcy’s relation is proposed. The results of this finite element model are independent of the original discretisation, as is demonstrated by an example of shear banding in a biaxial, plane-strain specimen.

A Spectral Finite Element Model for Wave Propagation Analysis in Laminated Composite Plate

Abstract: A new spectral plate element (SPE) is developed to analyze wave propagation in anisotropic laminated composite media. The element is based on the first-order laminated plate theory, which takes shear deformation into consideration. The element is formulated using the recently developed methodology of spectral finite element formulation based on the solution of a polynomial eigenvalue problem. By virtue of its frequency-wave number domain formulation, single element is sufficient to model large structures, where conventional finite element method will incur heavy cost of computation. The variation of the wave numbers with frequency is shown, which illustrates the inhomogeneous nature of the wave. The element is used to demonstrate the nature of the wave propagating in laminated composite due to mechanical impact and the effect of shear deformation on the mechanical response is demonstrated. The element is also upgraded to an active spectral plate clement for modeling open and closed loop vibration control of plate structures. Further, delamination is introduced in the SPE and scattered wave is captured for both broadband and modulated pulse loading.

On finite element modelling of surface tension: Variational formulation and applications – Part II: Dynamic problems

Abstract: In Part I, a finite element model of surface tension has been discussed and used to solve some quasi-static problems. The quasi-static analysis is often required to find not only the initial shape of the liquid but also the static equilibrium state of a liquid body before a dynamic analysis can be carried out. In general, natural and industrial processes in which surface tension force is dominant are of dynamic nature. In this second part of this work, the dynamic effects will be included in the finite element model described in Part I. A fully Lagrangian finite element method is used to solve the free surface flow problem and Newtonian constitutive equations describing the fluid behaviour are approximated over a finite time interval. As a result the momentum equations are function of nodal position instead of velocities. The resulting ordinary differential equation is integrated using Newmark algorithm. To avoid overly distorted elements an adaptive remeshing strategy is adopted. The adaptive strategy employs a remeshing indicator based on viscous dissipation functional and incorporates an appropriate transfer operator. The validation of the model is performed by comparing the finite element solutions to available analytical solutions of a droplet oscillations and experimental results pertaining to stretching of a liquid bridge.

Error analysis of a finite element method for the Willmore flow of graphs

Abstract: In Theorem 2.2 the choice of the discrete initial value u0h needs to be modified in order to guarantee higher order convergence for ew(0) = ŵh(0) − wh(0). Instead of choosing the initial value u0h as the minimal surface projection û0h of the continuous initial value u0 according to (2.17), we proceed as follows: Let ŵ0h be the solution of (2.22) at time t = 0. We then define the discrete initial value u0h as the solution of the equation ∫

A simple finite element model for vibration analyses induced by moving vehicles

Abstract: This study developed a simple finite element method combining the moving wheel element, spring-damper element, lumped mass and rigid link effect to simulate complicated vehicles. The advantages of this vehicle model are (1) the dynamic matrix equation is symmetric, (2) the theory and formulations are very simple and can be added to a standard dynamic finite element codes easily and (3) very complicated vehicle models can be assembled using the proposed elements as simple as the traditional finite element method. The Fryba's solution of a simply supported beam subjected to a moving two-axle system was analysed to validate this finite element model. For a number of numerical simulations, the two solutions are almost identical, which means that the proposed finite element model of moving vehicles is considerably accurate. Field measurements were also used to validate this vehicle model through a very complicated finite element analysis, which indicates that the current moving vehicle model can be used to simulate complex problem with acceptable accuracy.

The partition of unity finite element method for short wave acoustic propagation on non‐uniform potential flows

Abstract: A novel numerical method is proposed for modelling time-harmonic acoustic propagation of short wavelength disturbances on non-uniform potential flows. The method is based on the partition of unity finite element method in which a local basis of discrete plane waves is used to enrich the conventional finite element approximation space. The basis functions are local solutions of the governing equations. They are able to represent accurately the highly oscillatory behaviour of the solution within each element while taking into account the convective effect of the flow and the spatial variation in local sound speed when the flow is non-uniform. Many wavelengths can be included within a single element leading to ultra-sparse meshes. Results presented in this article will demonstrate that accurate solutions can be obtained in this way for a greatly reduced number of degrees of freedom when compared to conventional element or grid-based schemes. Numerical results for lined uniform two-dimensional ducts and for non-uniform axisymmetric ducts are presented to indicate the accuracy and performance which can be achieved. Numerical studies indicate that the pollution effect associated with cumulative dispersion error in conventional finite element schemes is largely eliminated.

Finite element based reduction methods for static and dynamic analysis of thin-walled structures

Abstract: Nonlinear Finite Element (FE) analysis receives growing attention in industrial and research applications. Modern computer facilities together with state of the art commercial finite element programs allow large and complicated analysis to be per­formed. The nonlinearities of the structural behavior are more and more often taken into account. However, the repeated solution in time of large nonlinear systems of equations stemming from a FE discretization to reproduce the static and dynamic behavior of a general structure is still a computationally intensive task. In the present thesis methods are presented that reduce the number degrees of freedom so that the computational cost is significantly reduced, while a sufficient accuracy of the analysis result is retained. Slender and thin­walled structures constitute main structural components in various engineering areas since they feature a high strength­to­weight and stiffness­to­weight ratio. These structures are prone to function at high displacement levels when subjected to operational loads, while staying in the material linear elastic range. The subject of this thesis is therefore confined to slender and thin­walled structures subjected to static and dynamic loads that trigger geometrical nonlinearities only.

Structural reliability analysis using deterministic finite element programs

Abstract: THE PAPER SHOWS HOW STRUCTURAL RELIABILITY ALGORITHMS CAN BE INCORPORATED INTO DETERMINISTIC (COMMERCIAL) FINITE ELEMENT CODES AND USED TO PERFORM NUMERICAL STRUCTURAL RELIABILITY ANALYSIS BASED ON FINITE ELEMENT MODELS OF A STRUCTURE. A STRUCTURAL RELIABILITY MODULE IS DEVELOPED AND LINKED TO THE ANSYS FINITE ELEMENT PROGRAM, CREATING A CUSTOMIZED VERSION OF THE PROGRAM. STRUCTURAL RELIABILITY ANALYSIS CAN BE PERFORMED IN THE ANSYS ENVIRONMENT, AND INVOLVES CONSTRUCTION OF A PARAMETRIC ¯NITE ELEMENT MODEL, DEFINITION OF RANDOM PARAMETER DISTRIBUTIONS, DE¯NITION OF A LIMIT STATE FUNCTION BASED ON FINITE ELEMENT RESULTS, AND SOLUTION FOR THE FAILURE PROBABILITY. NUMERICAL EXAMPLES INVOLVING TRUSS AND FRAME STRUCTURES ARE STUDIED. AN APPLICATION EXAMPLE - STRUCTURAL RELIABILITY ANALYSIS OF AN EYE-BAR USPENSION BRIDGE - IS ALSO PRESENTED.

Vibration Analysis of Rotating Tapered Timoshenko Beams by a New Finite Element Model

Abstract: A new finite element model is developed and subsequently used for transverse vibrations of tapered Timoshenko beams with rectangular cross-section. The displacement functions of the finite element are derived from the coupled displacement field (the polynomial coefficients of transverse displacement and cross-sectional rotation are coupled through consideration of the differential equations of equilibrium) approach by considering the tapering functions of breadth and depth of the beam. This procedure reduces the number of nodal variables. The new model can also be used for uniform beams. The stiffness and mass matrices of the finite element model are expressed by using the energy equations. To confirm the accuracy, efficiency, and versatility of the new model, a semi-symbolic computer program in MATLAB® is developed. As illustrative examples, the bending natural frequencies of non-rotating/rotating uniform and tapered Timoshenko beams are obtained and compared with previously published results and the results obtained from the finite element models of solids created in ABAQUS. Excellent agreement is found between the results of new finite element model and the other results.