Nonlinear finite element analysis of curved beams

Mixed curved-beam finite elements are developed for the geometrically nonlinear analysis of deep arches. The analytical formulation is based on a form of the nonlinear deep-arch theory with the effects of transverse shear deformation and bending-extensional coupling included. The fundamental unknowns consist of the six internal forces and generalized displacements of the arch. The generalized stiffness matrix is obtained by using a modified form of the Hellinger-Reissner mixed variational principle. Numerical studies are presented to demonstrate the high accuracy of the solutions obtained by the mixed models and to show that their performance is considerably less sensitive to variations in the arch geometry than that of the displacement models.     

Nonlinear analysis of skew plates using the finite element method

In this paper finite element analysis of the large deflection behaviour of skew plates has been done. A high precision conforming triangular plate bending element has been used. The central deflection, bending and membrane stresses have been reported for simply supported and clamped rhombic plates. The variations of these quantities have been studied for different skew angles.     

Nonlinear finite element analysis of shell structures using the semi-loof element

The Semi-Loof Shell element originally developed by Irons [2] for linear elastic analysis of thin shell structures is formulated to include large deflection and plastic deformation effects. In this paper the details of the finite element formulation of the problem using total Lagrangian coordinate systems are presented and different element matrices are given. For plastic materials following the Prandtl-Reuss flow rule with isotropic strain hardening a multi-layer approach using a subincremental technique is employed. Numerical results on the performance of the element for a variety of applications are presented. These computer studies include complete load-deflection curves into the post-buckling range and comparisons are made with other existing results. Current experience with the element indicates that it is a reliable and competitive element for nonlinear analysis of shells of general geometry.     

On an equilibrium finite element method for plate bending problems

A mathematical analysis of the so called «equilibrium» finite element method is carried out. Convergence of the scheme and optimal error bounds are proved.     

The analysis of composite beams using standard finite element programs

The paper describes how a model using only standard finite elements can be made equivalent to a connecting system in composite construction. Using standard elements and not special slip elements enables composite construction to be analysed by the standard finite element packages now widely available. The method is applied to both the elastic analysis and ultimate load analysis of composite beams and gives results in close agreement to either experimental or other established analytical results.     

Lateral buckling of locally buckled beams using finite element techniques

This paper deals with lateral-torsional buckling of beams which have already buckled locally before the occurrence of overall buckling. Due to the weakening effects of local buckling, the stiffness of the beam is reduced. As a result, overall lateral buckling takes place at a lower load than the member would carry in the absence of local buckling. The effective width concept is used in this investigation to account for the post-buckling strength in the buckled compression plate elements of the beam section. A finite element formulation in conjunction with effective width concept is presented. Due to the nonlinearity involved because of local buckling, an iterative procedure is necessary. Search techniques are used to find the load factor. The method combined with an analysis on nonlinear bending moment distribution can be used to analyze the lateral stability problem of locally buckled continuous structure. In this case, both elastic stiffness matrix and geometric stiffness matrix must be revised at each load level. A computer program has been prepared for an IBM 370/165 computer.     

Topology optimization using the p-version of the finite element method

A multiresolution topology optimization approach is proposed using the p-version finite element method (p-version FEM). Traditional topology optimization, where a density design variable is assigned to each element, is suitable for low-order h-version FEM. However, it cannot take advantage of the higher accuracy of higher-order p-version FEM analysis for generating results with higher resolution. In contrast, the proposed method separates density variables and finite elements so that the resolution of the density field, which defines the structure, can be higher than that of the finite element mesh. Thus, the method can take full advantage of the higher accuracy of p-version FEM.     

Elastic-plastic analysis of composite beams with incomplete interaction by finite element method

This paper presents a nonlinear finite element analysis of composite beams with incomplete interaction. A simplified nonlinear model is assumed in this approach. This is applied to the elastic-plastic analysis of reinforced concrete beams and composite beams with incomplete interaction. The numerical results are compared with the test results and existing values based on other numerical methods, and found to be in good agreement. The elastic-plastic behavior of partial composite beams without shear connectors in the negative bending moment region is discussed by the proposed method.     

A powerful finite element for plate bending

A powerful finite element formulation for plate bending has been developed using a modified version of the variational method of Trefftz. The notion of a boundary has been generalized to include the interelement boundary. All boundary conditions and the interelement continuity requirements (displacements, slopes, internal forces) have been obtained as natural conditions on the generalized boundary. Coordinate functions have been constructed to satisfy the nonhomogeneous Lagrange equation locally within the elements. Singularities due to isolated loads have been properly taken into account. For practical use a general quadrilateral element has been developed and its accuracy illustrated on several numerical examples. Work is in progress to extend the formulation to anisotropic and moderately thick plates and to vibration analysis.     

Nonlinear dynamics of viscoelastic flexible structural systems by finite element method

This article presents a nonlinear displacement based finite elements model to study and analyze the nonlinear dynamic response of flexible double wishbone structural vehicle suspension system considering damping effect which was not previously discussed elsewhere. Due to large deflection and moderate rotation encountered during passing over road bumps, the kinematic nonlinearity is included through von Kármán strain component. Elastic undamped as well as viscous and viscoelastic damping mechanism are considered and compared. Considering the viscoelastic damping mechanism, the viscoelastic damping mechanism is modeled based on the integral constitutive form, which is recast into an incremental form suitable for finite element implementation. Additionally, the revolute joint element is adopted to incorporate the joint flexibility in the double wishbone system. The plane frame element is adopted to model the suspension links by using Timoshenko beam theory. The developed nonlinear finite element equations of motion are solved through the incremental iterative Newmark technique. The developed procedure is verified by comparing the obtained results with analytical solution and excellent agreement is observed. The applicability of the developed procedure is demonstrated by conducting parametric studies to show the effects of the road irregularities profiles, the vehicle speed, and the material damping coefficients on the nonlinear vibrations response of the double wishbone suspension systems. The obtained results are supportive in the design and manufacturing processes of these structural systems.

     

A finite element method for elastic-plastic beams and columns at large deflections

A finite element scheme for the large-displacement analysis of elastic-plastic beams and columns is presented. The proposed method, which assures continuous deflections and continuous slopes at the element junctions, is shown to furnish fairly accurate results with a minimal number of elements. Comparisons are made with existing results for laterally loaded beams on elastic foundations and for elastic columns on bi-linear elastoplastic foundations. The effect of imperfections on the buckling of elastic-plastic columns is also investigated.     

Electromagnetic design of microwave filters using the finite element method

We present two complex microwave filter designs using the finite element method (FEM). A metallic cavity, loaded by low-loss dielectric plates is first optimized to obtain a high unloaded quality factor resonator. An original synthesis approach is then proposed to design a three-pole dielectric loaded cavity filter. The FEM is also applied to characterize a filter element, a dielectric resonator (DR) coupled on a whispering gallery mode (WGM) to two microstrip lines. A generalized [S] matrix is computed. Different elements are then put together to generate complex filtering responses. © 1997 John Wiley & Sons, Inc. Int J Microwave Millimeter-Wave CAE 7: 167–179, 1997.     

Nonlinear finite element analysis of concrete structures using new constitutive models

Nonlinear finite element analysis was applied to various types of reinforced concrete structures using a new set of constitutive models established in the fixed-angle softened-truss model (FA-STM). A computer code FEAPRC was developed specifically for application to reinforced concrete structures by modifying the general-purpose program FEAP. FEAPRC can take care of the four important characteristics of cracked reinforced concrete: (1) the softening effect of concrete in compression, (2) the tension-stiffening effect by concrete in tension, (3) the average (or smeared) stress–strain curve of steel bars embedded in concrete, and (4) the new, rational shear modulus of concrete. The predictions made by FEAPRC are in good agreement with the experimental results of beams, panels, and framed shear walls.     

A finite element model for thick beams

A general method for obtaining higher order beam theories is reviewed and cast in a form for creating a finite element model. Reissner's principle and Legendre polynomial series expansions are key features in the development. A thick beam element is produced having capabilities of representing nonlinear distributions, through the thickness, of all stress and deformation variables. The model can be used to analyze most thick beams and localized stress conditions. Beam problems are solved and the performance of the thick beam element model is assessed.     

在裂纹尖端引入奇异单元的偶应力有限元法

针对在微观状态下结构力学行为会受尺度效应影响的问题,在偶应力理论中考虑微观结构的旋转梯度可以较好解释结构的尺度效应.建立基于一般偶应力理论的有限元法的基本方程,并在裂纹尖端引入奇异单元,计算受单向拉伸的中心斜裂纹板裂纹尖端场的应力强度因子(Stress Intensity Factor,SIF),分析特征长度变化对SIF的影响,对比偶应力理论下的结果与经典理论下的结果.结果表明：在裂纹尖端引入奇异单元可以提高计算精度和稳定性;偶应力使得裂纹尖端SIF比经典理论下的值小,并且SIF随着特征长度增大而减小.     

Optimal control of inverted pendulums using finite element method

An alternative control scheme based on finite element method has been developed to solve optimal control problems in space and time domains. The nonlinear Lagrangian is expanded about a given trajectory configuration in terms of a correction vector. The equations of motion are derived retaining only upto quadratic terms. The cost function comprises of total absolute torsional impulse and equations of motion are the constraints. The control of simple and double inverted pendulums is presented here to show the validity of this method. These problems are also solved using the classical Riccati method for comparison.     

Damage detection of structures using spectral finite element method

This paper brings together the principles, equations, and applications of damage modelling and elastic waves propagation, both traditional and state-of-the-art in a review form. It begins with the relevant fundamentals of damage modelling, derives the basic equations of fracture mechanics and elastic wave propagations, and covers advanced topics and applications of Lamb waves that are at the forefront of today’s research. The results obtained indicate that the current approach is capable of detecting cracks and delaminations of very small size, even in the presence of considerable measurement errors. The sections are filled with case studies, worked examples and exercises that make this paper an outstanding resource.     

Three-dimensional mesh generation using principles of finite element method

The present work deals with the development of a three-dimensional mesh generation algorithm using the principles of FEM with special emphasis on the computational efficiency and the memory requirement. The algorithm makes use of a basic mesh that defines the total number of elements and nodes. Wavefront technique is used to renumber the nodes in order to reduce the bandwidth. By elastic distortion of the basic mesh, it is redefined to map onto actual geometry to be discretized. Later a finer distribution of mesh is done in the zones of interest to suit the nature of the problem. The same Finite Element code meant for stress analysis is adopted with necessary modifications. The algorithm has been extended to three-dimensional geometries. The current methodology is used to discretize a straight bevel gear and an hourglass worm to study their stress patterns.     

Optimization design of multi-material micropump using finite element method

This paper presents a micropump fabricated from low cost materials with specific goal of cost reduction. The micropump does not require any valve flap and comprises one plastic pump polyether–ether–ketone (PEEK) body, one metal diaphragm, and three piezoelectric ceramics to form piezoelectrically actuated diaphragm valves. The valve actuation simplifies micropump structural designs and assembly processes to make the pump attractive for low cost bio-medical drug delivery applications. A detailed optimization design of geometric parameters of the piezoelectrically actuated diaphragm is undertaken by use of 3D finite element method (FEM) to maximize piezoelectric actuation capability and ensure actuation reliability. An optimized geometric dimensional design: the ratio of thicknesses between the piezoelectric ceramics and the metal diaphragm, and the lateral dimension of the piezoelectric ceramic, is obtained through simulations. Based on the optimized design, a good agreement has been reached between simulated and measured strokes of the micropumps. The tested results show that the micropump has a high pump flow rate for air, up to 39 ml/min, and for water, up to 1.8 ml/min, and is capable of ensuring diaphragm’s maximum stress and strain is within material strength for reliable work.