Finite element analysis

Current use of the finite element method in engineering practice is considered. The increasing use of finite element analysis in a CAD environment and factors influencing it are discussed.The technological state of the art is briefly reviewed. Special consideration is given to shell elements and solution methods, illustrating the progress being made in these and other areas of finite element technology. Future trends are predicted.     

Finite element analysis of shell structures

Summary A survey of effective finite element formulations for the analysis of shell structures is presented. First, the basic requirements for shell elements are discussed, in which it is emphasized that generality and reliability are most important items. A general displacement-based formulation is then briefly reviewed. This formulation is not effective, but it is used as a starting point for developing a general and effective approach using the mixed interpolation of the tensorial components. The formulation of various MITC elements (that is, elements based on Mixed Interpolation of Tensorial Components) are presented. Theoretical results (applicable to plate analysis) and various numerical results of analyses of plates and shells are summarized. These illustrate some current capabilities and the potential for further finite element developments.     

Finite element analysis of suspension bridges

A finite element analysis of static and dynamic response of suspension bridges is presented in this paper. Several finite element models of the three-dimensional bridge structure, with varying degrees of complexity and accuracy, are discussed. The formulation takes into account the geometric nonlinearities of the cables and some elements of the girders-bracingsdeck system as well as the nonlinear material properties of the components. Special attention is given to the effects of steady and unsteady wind forces. Examples of application include calculations of the static and dynamic response of a bridge subjected to wind and moving loads.     

Finite element analysis of stiffened plates

A finite element method is presented in which the constraint between stiffener and member is imposed by means of Lagrange multipliers. This is performed on the functional level, forming augmented variational principles. In order to simplify the initial development and implementation of the proposed method, two-dimensional stiffened beam finite elements are developed. Several such elements are formulated, each showing monotonic convergence in numerical tests. In the development of stiffened plate finite elements, the bending and membrane behaviors are treated seperately. For each, the stiffness matrix of a standard plate element is modified to account for an added beam element (representing the stiffener) and additional terms imposing the constraint between the two. The resulting stiffened plate element was implemented in the SAPIV finite element code. Exact solutions are not known for rib-reinforced plated structures, but results of numerical tests converge monotonically to a value in the vicinity of an approximate “smeared” series solution.     

Finite element analysis with uncertain probabilities

This paper presents a general method for the finite element analysis of linear mechanical systems by taking into account probability density functions whose parameters are affected by fuzziness. Within this framework, the standard perturbation-based stochastic finite element method is relaxed in order to incorporate uncertain probabilities in static, dynamic and modal analyses. General formulae are provided for assessing the (fuzzy) structural reliability and several typologies of optimization problems (reliability-based design, robust design, robust/reliability-based design) are formalized. In doing this the credibility theory is extensively used to extract qualified crisp data from the available set of fuzzy results, so that standard optimizers can be adopted to solve the most important design problems. It is shown that the proposed methodology is a general and versatile tool for finite element analyses because it is able to consider, both, probabilistic and non-probabilistic sources of uncertainties, such as randomness, vagueness, ambiguity and imprecision.     

Finite element analysis of shock-induced hull cavitation

The paper describes the theoretical formulation and computational implementation of a method for treating hull cavitation in underwater-shock problems. In addition, the method can be applied to the analysis of submerged structures that contain internal fluid volumes. In the present implementation, the Doubly Asymptotic Approximation (DAA) serves to simulate a radiation boundary that is located away from the fluid-structure surface at a distance sufficient to contain any cavitating region. The enclosed fluid is discretized with volume finite elements that are based upon a displacement-potential formulation. An explicit time-integration algorithm is used to advance the solution in the fluid-volume region, implicit algorithms are used for the structure and DAA boundary, and a staggered solution procedure has been developed to treat the interface conditions. Results for two example problems obtained with the present implementation show close agreement with those obtained by other methods.     

Finite element analysis of nonlinear magnetic fields

The basic equations of electromagnetism are written in the form of a quasi-harmonic equation. The application of the weighted residual process leads to a non-linear system of algebraic equations which is solved by a full Newton–Raphson procedure. The iteration scheme is developed and applied to numerical examples.     

Finite element analysis of laminated shells of revolution

A finite element formulation for the analysis of axisymmetric fibre reinforced laminated shells subjected to axisymmetric load is presented. The formulation includes arbitrary number of bonded layers each of which may have different thicknesses, orientation of elastic axes, and elastic properties. Superparamatric curved elements[17] having four degrees of freedom per node including the normal rotation, are used. Stress-strain relation for an arbitrary layer is obtained from the consideration of three dimensional aspect of the problem. The element stiffness matrix has been obtained by using Gauss quadrature numerical integration, even though the elasticity matrix is different for different layers. The formulation is checked for a cylindrical tube subjected to internal pressure and axial tension, and the results are found to compare very well with the elastic solution [9].     

Finite element analysis of composites using chebyshev polynomials

A finite quasi-prismatic (FQP) element is modified to analyze anisotropic materials. The finite quasi-prismatic element is a three-dimensional finite element which uses conventional interpolating functions in two directions and functions based on Chebyshev polynomials in the third direction. This element is used to solve different anisotropic problems and the results are compared with that of conventional finite elements and analytical solutions.     

Finite element analysis of laminated composite shell junctions

The axisymmetric bending of laminated composite shell junctions have been analysed by the finite element displacement method using laminated anisotropic shell theory. Numerical results have been presented for cylinder-cone shell junction and cylinder-geodesic-isotensoid dome junction. These results have been compared with results for isotropic case.     

Finite element bending analysis of nonuniform circular plates

The finite element method is applied to the small deflection bending analysis of nonuniform thin axisymmetric circular plates made of linear elastic material. Elements with annular and circular geometry with only 4 degrees of freedom are used in the analysis of both symetrically and nonsymmetrically loaded plates. Non-symmetric loads are expanded in Fourier series and elements restricted to deform with specified number of nodal diameters are used for each component of loading. The method is checked with several numerical examples. Although applicable to only axisymmetric plates, the method gives better results compared to other finite element methods besides offering savings in computer storage and time.     

Finite element analysis of steadily moving contact fields

By introducing a moving updated Lagrangian observer, this paper develops traveling finite elements with the capacity to handle the global response resulting from steadily moving contact fields. The generality of the results is such that large deformation kinematics and kinetics as well as the full compliment of inertial fields can be handled. To streamline the handling of nonlinear behavior, an elliptically constrained solution algorithm is also developed. Employing this algorithm, the results of several numerical benchmarking studies are presented which illustrate the capacity of the moving updated Lagrangian formulation as well as the potential effects of nonlinearity.     

Finite element analysis of maneuvering spacecraft truss structures

A finite element modeling and solution technique capable of determining the time response of flexible spacecraft truss structures undergoing large angle slew maneuvers has been developed. The elastic deformations of the structure are coupled with large nonsteady translational and rotational motions with respect to an inertial reference frame. The governing equations of motion of the system are derived using momentum conservation principles and the principle of virtual work. The finite element approximation is applied to the equations of motion and the resulting set of nonlinear second order matrix differential equations is solved timewise by an iterative direct numerical integration scheme based on the trapezoidal rule. The solution technique is tested on both planar and three-dimensional maneuvering spacecraft truss structures.     

Finite element analysis of the captive column structure

A linearly elastic finite element computer model is developed for analyzing the behavior of a structural member concept known as the “captive column.” This concept has the potential for combining high-strength and lightweight materials in optimum configurations to produce structural components fora variety of applications. Experimental verification of the computer model is presented for the case of static flexural loading of captive column members acting as beams. Both deflection and stress results are compared. The computer model is shown to hold promise as a useful design tool for specific applications of the captive column concept.     

Finite element analysis of the shear vane test

Finite element analyses of the standard shear vane test to measure the in situ undrained shear strength of soil are presented. The mobilization of shear stresses on the vertical and horizontal faces of the vane has been studied up to failure and compared with analytical solutions. This has been achieved by the use of 2-D and quasi-3-D analyses. Good agreement between the computed and analytical solutions was achieved provided the soil strength was isotropic. The influence of soil strength anisotropy was considered by the use of a simple model in which the undrained shear strength was related to direction. The effect of strain softening was also incorporated into the analyses. When combined with the quasi-3-D analysis, these features allowed more realistic models to be made of the shear strength mobilization on all parts of the cylindrical failure surface.     

Solving Wick-stochastic water waves using a Galerkin finite element method

A Galerkin finite element approximation of Wick-stochastic water waves is developed and numerically investigated. The problems under study consist of a class of shallow water equations driven by white noise. Random effects may appear in the water free surface or in the bottom topography among others. To perform a rigorous study of stochastic effects in the shallow water equations we employ techniques from Wick calculus. The differentiation respect to time and space along with the product operations are performed in a distribution sense. Using the Wiener-Itô chaos expansion for treating the randomness, the governing equations are transformed into a sequence of deterministic shallow water equations to be solved for each chaos coefficient by standard methods from computational fluid dynamics. In our study, we formulate a finite element method for spatial discretization and a backward Euler scheme for time integration. Once the chaos coefficients are obtained, statistical moments for the stochastic solution are carried out. Numerical results are presented for stochastic water waves in the Strait of Gibraltar.     

平板式轧制力传感器的有限元分析

利用有限元分析软件ANSYS Workbench对平板式轧制力传感器的弹性体进行了分析,解决了弹性体深孔的贴片深度问题,并且研究了弹性体内部结构尺寸变化对贴片区输出应变的影响,为优化设计提供了依据,加快了产品研发的进度。     

Finite element stress formulation for dynamic elastic-plastic analysis

The solution to wave propagation problems in solids with elastic-plastic material properties is obtained by using the finite element method directly in terms of the stresses. A variational principle due to Gurtin is modified by including a plastic strain tensor in the constitutive relationship. The resulting finite element equations, which represent the strain-displacement equations written in terms of the stresses, are simultaneous integral equations in time. With a transformation of variables, a set of simultaneous differential equations is obtained of the form$\text{H}\text{s}\text{?}\text{+ Qs+ Ve}{}_{\mathrm{p}}\text{= q(t)}$, where $\text{H}$ is a symmetric positive-semidefinite matrix, and $\text{Q}$ is a symmetric positive-definite matrix. The stresses and the plastic strains are represented by $\text{s}\text{?}$ and $\text{e}{}_{\mathrm{p}}$, respectively.Finite element equations are developed for an axisymmetric ring element with an arbitrary quadrilateral cross section in which the stresses and the plastic strains vary linearly along the sides of the elements. The equations are numerically integrated with respect to time by Newmark's generalized acceleration method.An iterative procedure is presented, which uses the finite element strain-displacement equations and the plasticity relationships, to determine the state of stress at the end of the time step. Several examples are used to demonstrate the solution technique for elastic and elastic-plastic problems.