脱层板固有频率的有限元方法分析

结合弹性材料修正后的H-R(Hellinger-Reissner)变分原理和二次插值函数,建立了平面坐标系下Hamilton正则方程推导了八节点等参元列式.考虑到脱层板的连接界面上应力和位移的连续性,将脱层板离散成上下两层,采用"分离合并"技术,建立脱层情况下板的控制方程.本文具体研究了脱层结构的固有频率问题,数值实例证明了本文方法的正确性.八节点等参元的使用不仅减少了节点数,同时也大大提高了计算效率.     

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.     

A parallel finite element procedure for contact-impact problems

An efficient parallel finite element procedure for contact-impact problems is presented within the framework of explicit finite element analysis with thepenalty method. The procedure concerned includes a parallel Belytschko-Lin-Tsay shell element generation algorithm and a parallel contact-impact algorithm based on the master-slave slideline algorithm. An element-wise domain decomposition strategy and a communication minimization strategy are featured to achieve almost perfect load balancing among processors and to show scalability of the parallel performance. Throughout this work, a prototype code, named GT-PARADYN, is developed on the IBM SP2 to implement the procedure presented, under message-passing paradigm. Some examples are provided to demonstrate the timing results of the algorithms, discussing the accuracy and efficiency of the code.     

Three-dimensional finite element analysis of thick laminated plates

A displacement-based, three-dimensional finite element scheme is proposed for analyzing thick laminated plates. In the present formulation, a thick laminated plate is treated as a three-dimensional inhomogeneous anisotropic elastic body. Particular attention is focused on the prediction of transverse shear stresses. The plane of a laminated plate is first discretized into conventional eight-node elements. Various through-thickness interpolation is then denned for different regions of the plate; layerwise local shape functions are used in the regions where transverse shear stresses are of interest, while an ad hoc global-local interpolation is used in the region where only the general deformation pattern is concerned. For satisfying the displacement compatibility between these two regions, a transition zone is introduced. The model incorporates the advantages of the layerwise plate theory and the single-layer plate theory. Details of formulation will be presented together with several numerical examples for demonstrating the proposed scheme.     

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.     

Finite element analysis of laminated anisotropic beams of bimodulus materials

This paper presents finite element analysis of laminated anisotropic beams of bimodulus materials. The finite element has 16 d.o.f. and uses the displacement field in terms of first order Hermite interpolation polynomials. As the neutral axis position may change from point to point along the length of the beam, an iterative procedure is employed to determine the location of zero strain points along the length. Using this element some problems of laminated beams of bimodulus materials are solved for concentrated loads/moments perpendicular and parallel to the layering planes as well as combined loads.     

Non-linear finite element analysis of composite beams with interlayer slips

This article presents a new non-linear finite element formulation for the analysis of two-layer composite plane beams with interlayer slips. The element is based on the corotational method. The main interest of this approach is that different linear elements can be automatically transformed to non-linear ones. To avoid curvature locking that may occur for low order element(s), a local linear formulation based on the exact stiffness matrix is used. Five numerical applications are presented in order to assess the performance of the formulation.     

Geometrically nonlinear finite element analysis of tapered beams

A novel finite element methodology is developed capable of analyzing the geometrically nonlinear behavior of thin-walled framed structures composed of non-prismatic members. The pertinent element matrices are formulated on the basis of a modified version of the variational theorem of Hellinger and Reissner. Finite geometry changes are consistently described by using an updated Lagrangian (U.L.) formulation. Validity, accuracy and reliability of the proposed scheme are examined on the basis of several well-selected test examples.     

A finite element method for a class of contact-impact problems

We present a finite element method for a class of contact-impact problems. Theoretical background and numerical implementation features are discussed. In particular, we consider the basic ideas of contact-impact, the assumptions which define the class of problems we deal with, spatial and temporal discretizations of the bodies involved, special problems concerning the contact of bodies of different dimensions, discrete impact and release conditions, and solution of the nonlinear algebraic problem. Several sample problems are presented which demonstrate the accuracy and versatility of the algorithm.     

Analysis of laminated shells of revolution with laminated stiffeners using a doubly curved quadrilateral finite element

A finite element analysis of laminated shells of revolution reinforced with laminated stifieners is described here-in. A doubly curved quadrilateral laminated anisotropic shell of revolution finite element of 48 d.o.f. is used in conjunction with two stiffener elements of 16 d.o.f. namely: (i) A laminated anisotropic parallel circle stiffener element (PCSE); (ii) A laminated anisotropic meridional stiffener element (MSE).These stifiener elements are formulated under line member assumptions as degenerate cases of the quadrilateral shell element to achieve compatibility all along the shell-stifiener junction lines. The solutions to the problem of a stiffened cantilever cylindrical shell are used to check the correctness of the present program while it's capability is shown through the prediction of the behavior of an eccentrically stiffened laminated hyperboloidal shell.     

Nonlinear bending of beams using the finite element method

In this paper a finite element formulation for determining the finite deflection of thin bars is presented. The nonlinear stiffness equations are generated after simple approximate expressions involving the nodal parameters are used to replace the nonlinear terms in the energy functional. The procedure used results in a simplified set of nonlinear algebraic equations which are more amenable to solution than the equations usually presented. The applicability and accuracy of the method together with an evaluation of three incremental solution techniques, a step by step method, a one step Newton-Raphson procedure, and a variable interpolation technique is demonstrated by solving a cantilever beam with a point load acting on the end. Curves showing the sensitivity to increment size and to the number of elements are also presented. The results indicate that the formulation is accurate and inexpensive in terms of computational effort.     

Estimation of low-velocity impact damage in laminated composite circular plates using nonlinear finite element analysis

Nonlinear finite element analysis is used for the estimation of damage due to low-velocity impact loading of laminated composite circular plates. The impact loading is treated as an equivalent static loading by assuming the impactor to be spherical and the contact to obey Hertzian law. The stresses in the laminate are calculated using a 48 d.o.f. laminated composite sector element. Subsequently, the Tsai-Wu criterion is used to detect the zones of failure and the maximum stress criterion is used to identify the mode of failure. Then the material properties of the laminate are degraded in the failed regions. The stress analysis is performed again using the degraded properties of the plies. The iterative process is repeated until no more failure is detected in the laminate. The problem of a typical T300/N5208 composite [45 °/0 °/ − 45 °/90 °]_s circular plate being impacted by a spherical impactor is solved and the results are compared with experimental and analytical results available in the literature. The method proposed and the computer code developed can handle symmetric, as well as unsymmetric, laminates. It can be easily extended to cover the impact of composite rectangular plates, shell panels and shells.     

Dynamic characterization of thin-walled laminated channel beams with warping

The dynamic characteristics of a round cornered C-channel beam made of laminated composite material are studied. The sharp corners are rounded for manufacturing considerations. Thin-walled beam theory is used to formulate the coupled vibration of a rounded C-channel beam with fixed-free end conditions. It is shown that cross-sectional properties used for isotropic case are applicable for laminated composites and the material properties needed for the formulation can be obtained using the law of average. A comparative study is conducted to show the advantage of using composites. The effect of radius of corner and warping on the natural frequency is investigated. The functional of the equations of motion is formed using the variational method. The Ritz method has been used to formulate an eigenvalue problem and its frequency equation. The method proposed is systematic. The computerized procedure can be used as a fast design tool in the design of composite channel beam structures.     

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.     

A finite element analysis of deep beams with cutouts considering four supports

Using the finite element method, the biaxial stress distribution has been determined for a wide-flange deep beam, with rectangular cutouts placed at various locations, on four supports. An elastic plane state of stress is assumed for the web of the beam and an elastic uniaxial state of stress is assumed for the flanges. The influence that cutouts indeterminate supports have on the stress distribution in deep beams is illustrated by plotting the stress distribution, at several longitudinal locations, for the homogeneous beam and the beam with cutouts, on both determinate and indeterminate supports. Several convergence studies have been performed to determine the proper mesh sizes for the given problems.     

加速度传感器的有限元分析

为了分析加速度传感器的动态特性,对其进行了模态分析、频响和瞬态分析。通过模态分析得到传感器的前六阶固有频率和振型,频响分析和瞬态分析得到传感器的幅频特性,得出传感器动态维间耦合情况。仿真实验的结果表明:传感器一阶和二阶、四阶和五阶振型相同,频率相近;传感器受到轴向载荷的时候,轴向与水平方向存在较大的动态耦合;受到水平方向载荷作用时轴向耦合较大,而与另一水平方向耦合较小。     

Dynamic finite element analysis of nonaxisymmetric structures

A dynamic finite element method of analysis is developed for structural configurations which are derived from axisymmetric geometries but contain definite nonaxisymmetric features in the circumferential direction. The purpose of the analysis is to develop a method which will take into consideration the fact that the stress and strain conditions in these geometries will be related to the corresponding axisymmetrie solution. This analysis is an extension of previously published work in which a similar approach was developed for static structural problems. The analysis is developed in terms of a cylindrical coordinate system r, θ and z. As the first step of the analysis, the geometry is divided into several segments in the r-θ plane. Each segment is then divided into a set of quadrilateral elements in the r-z plane. The axisymmetric displacements are obtained for each segment by solving a related axisymmetric configuration. A perturbation analysis is then performed to match the solutions at certain points between the segments, and obtain the perturbation displacements for the total structure. The total displacement is then the axisymmetric displacement plus the perturbation displacement. The analysis allows for elastic-plastic materials with orthotropic yield criterion based on Hill's yield function and kinematic strain hardening. The finite element dynamic equations are solved by finite differences by dividing the time domain into incremental steps. The solution has been programmed on a computer and applied to a number of examples.     

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 new heterosis plate element for geometrically non-linear finite element analysis of laminated plates

In this study, a new nine-node quadrilateral, shear-deformable heterosis element is developed. In order to model this element, Kirchhoff constraints are modified using Reissner-Mindlin theory assumptions. All of the modifications are performed for first-order shear-deformation theory (FSDT). This new heterosis element is developed by modifying 8-node serendipity and twelve-node cubic polynomials. The new heterosis element is used with nine-node Lagrangian elements in finite element analysis of composite plates. A modified element is used in finite element analysis of linear and non-linear analysis considering the advantages of free of ‘shear locking’. Numerical results are presented by comparing Navier's series solution.