摘要:

AbstractA formulation for the plane 4‐node quadrilateral finite element is developed based on the principle of virtual displacements for a deformable body. Incompatible modes are added to the standard displacement field. Then expressions for gradient operators are obtained from an expansion of the basis functions into a second‐order Taylor series in the physical co‐ordinates. The internal degrees of freedom of the incompatible modes are eliminated on the element level. A modified change of variables is used to integrate the element matrices.For a linear elastic material, the element stiffness matrix can be separated into two parts. These are equivalent to a stiffness matrix obtained from underintegration and a stabilization matrix.The formulation includes the cases of plane stress and plane strain as well as the analysis of incompressible materials. Further, the approach is suitable for non‐linear analysis. There, an application is given for the calculation of inelastic problems in physically non‐linear elasticity.The element is efficient to implement and it is frame invariant. Locking effects and zero‐energy modes are avoided as well as singularities of the stiffness matrix due to geometric distortion. A high accuracy is obtained for numerical solutions in displacements a

ISSN:0029-5981    

DOI:10.1002/nme.1620381802

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe standard plane 4‐node element is written as the summation of a constant gradient matrix, usually obtained from underintegration, and a stabilization matrix. The split is based on a Taylor series expansion of element basis functions. In the incompressible limit, the ‘locking’‐effect of the quadrilateral is traced back to the stabilization matrix which reflects the incomplete higher‐order term in the Taylor series.The incompressibility condition is formulated in a weak sense so that the element displacement field is divergence‐free when integrated over the element volume. The resulting algebraic constraint is shown to coincide with a particular eigenvector of the constant gradient matrix which is obtained from the first‐order terms of the Taylor series. The corresponding eigenvalue enforces incompressibility implicitly by means of a penalty‐constraint. Analytical expressions for that constant‐dilatation eigenpair are derived for arbitrary element geometries. It is shown how the incompressible constraint carries over to the element stiffness matrix if the element stabilization is performed in a particular manner.For several classical and recent elements, the eigensystems are analysed numerically. It is shown that most of the formulations reflect the incompressible constraint identically. In the incompressible limit, the numerical accuracies of the elem

ISSN:0029-5981    

DOI:10.1002/nme.1620381803

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThere are today as many finite element input languages as there are finite element programs. These input languages were developed to serve one purpose: to provide the analyst with the means to convey the necessary analysis and design criteria to specific finite element programs. They were not developed as general finite element model‐definition languages, and as a result their syntax and semantics are often unnatural and contrived. In this work we do not invent a new input language. Instead, we propose and evaluate the Contraint Logic Programming language CLP(ℛ) as a general finite element model‐definition and input lan

ISSN:0029-5981    

DOI:10.1002/nme.1620381804

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThis paper presents and discusses an Arnoldi‐based eigensolution technique for evaluating the complex natural frequencies and mode shapes from frequency dependent quadratic eigenproblems associated with vibration analysis of damped structures. The new solution technique is used in conjunction with a mixed finite element modelling procedure which utilizes both the polynomial and frequency dependent displacement fields in formulating the system matrices. This modelling provides the ability to represent a frequency dependent damping matrix in vibration analysis of skeletal systems.The eigensolution methodology presented here is based upon the ability to evaluate a specific set of parametrized curves for the non‐linear eigenvalue problem at given values of the parameter. Numerical examples illustrate that this method, used in conjunction with a secant interpolation, accurately evaluates the complex natural frequencies and modes of the quadratic non‐linear eigenproblem and verifies that the new eigensolution technique coupled with the mixed finite element modelling procedure is more accurate than the conventional finite element m

ISSN:0029-5981    

DOI:10.1002/nme.1620381805

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe merits and limitations of the Optimality Criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the OC design code that was developed for this purpose at the NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. It includes multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analysers, and analytical and numerical sensitivities. On the basis of the examples solved, the optimality criteria for general application were found to be satisfactory for problems with few active constraints or with small numbers of design variables. However, the OC method without stress constraints converged to optimum even for large structural systems. For problems with large numbers of behaviour constraints and design variables, the method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.

ISSN:0029-5981    

DOI:10.1002/nme.1620381806

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractAn adaptive process controlling the position of nodes on a surface mesh is presented. The control can depend on one (or more) criterion(ria) about element quality. The mesh is attached, through the concept of classification, to a geometric model issued by a computer aided design software. Thus, the surface domain is described by entities currently available in such systems, i.e. any free‐form patches like Non‐Uniform Rational B‐Spline or Bézier patches can be used, even if they are restricted. Multi‐connected surface domains can be treated using the same geometrical definition. The method described allows nodes to slide on a patch or jump from a patch onto another one. Such movements greatly improve the mesh quality with regard to a chosen criterion. Problems occurring with patch‐by‐patch meshing techniques when surfaces patches exhibit significant size differences are then overcome. The adaptation technique can be made independent of CAD data structures and meshing techniques, hence it constitutes the basis of a mesh manag

ISSN:0029-5981    

DOI:10.1002/nme.1620381807

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe transient response of a finite elastic plate, resting on an elastic half‐space, and subjected to moving loads is considered here. Both the cases of an elastic foundation alone, as well as a finite sized elastic plate resting on an elastic foundation are considered. The numerical methods employed are: (1) the time‐domain boundary element method for the elastic foundation and (2) a combination of the time‐domain boundary element method for the soil and the semi‐discrete finite element method for the finite sized elastic plate. Both constant as well as linear‐time‐interpolation schemes are included in the BEM. The integration is carried out analytically in time. The analytical solution for a moving point load on an infinite elastic plate resting on an elastic half‐space is derived here. This is used as a benchmark against which the present numerical solution is compared with. The accuracy of the numerical method is also verified by comparing the solutions with some existing numerical results; the comparison with the solutions based on a Winkler foundation model reveals the limitations of the applicability of such a model, especially in the cases of high velocities of the moving load. This is because neither the inertia of the foundation, nor the behaviour of the foundation as a continuum, can be properly accounted for in Winkler's model. A parametric study is conducted, and the influences of velocity of the moving load, load distribution, etc. on the dynamic response of the soil/runway system are investigated. Furthermore, the present computational method is applied to the problem of a transport airplane taxiing on a concrete pavement resting on a typical soil. The responses of pavements are presented for different taxii

ISSN:0029-5981    

DOI:10.1002/nme.1620381808

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractModelling of crack behaviour is an important topic when establishing realistic macroscopic constitutive relations for brittle materials, such as ceramics, concrete, rock, etc. Upon introducing discontinuous approximation of the continuum, a crack model is derived on the basis of the Rankine plasticity model and the fictitious crack concept of Hillerborget al.1The derivation results in a crack band relation, whose constitutive properties are based on failure kinematics that resemble the classical shear band concept. It appears that it is, essentially, the acoustic tensor that governs the constitutive relation for the crack band. This tensor has previously been analysed extensively to determine conditions for loss of ellipticity and possibility for discontinuous bifurcation in the rate of deformation field. In the present approach a similar analysis is carried out to determine conditions that characterize fracture initiation and crack band orientation. The model is implemented together with a mesh realignment strategy, and a solution advancement formulation, that ensures the crack propagates along critical interfacial directions. These directions depend on the actual stress state and are kept fixed after plastic localization (or cracking) has occurred. Hence, a ‘fixed crack’ model is obtained. Numerical results involving successive crack development as well as failure of concrete beams are presen

ISSN:0029-5981    

DOI:10.1002/nme.1620381809

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620381810

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620381811

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY