摘要:

AbstractThe first‐ and second‐order, small strain and moderate rotation, theories of anisotropic laminated plates are developed and numerically evaluated. Beginning with an assumed displacement field and introducing various order‐of‐magnitude assumptions, the governing equilibrium equations of laminated plates are derived from the principle of virtual displacements. The finite‐element formulation for the second‐order moderate rotation theory is developed, and numerical results are presented to evaluate the new plate theories in comparison with the von Kàrmàn plate theory with shear deformation. For comparison purposes, the 2‐D elasticity theory with full non‐linearity is also analysed using the finite element method. It is found that the second‐order theory with moderate rotations is closest to the 2‐D fin

ISSN:0029-5981    

DOI:10.1002/nme.1620330102

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractAn assumed‐stress hybrid/mixed 4‐node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed‐stress hybrid/mixed method using the Hellinger‐Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or ‘drilling’ degrees of freedom at the nodes. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner‐Mindlin plate theory which takes into account the transverse shear contributions. The element formulation is derived from an 8‐node isoparametric element by expressing the midside displacement degrees of freedom in terms of displacement and rotational degrees of freedom at corner nodes. The element passes the patch test, is nearly insensitive to mesh distortion, does not ‘lock’, possesses the desirable invariance properties, has no hidden spurious modes, and for the majority of test cases used in this paper produces more accurate results than the other elements employed he

ISSN:0029-5981    

DOI:10.1002/nme.1620330103

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractTheh‐pmethod for solving partial differential equations uses discretizations where the grid sizehand the polynomial degreepare varied to obtain the most efficiency in the computing of approximate solutions. It has been known for many years that increasingpcan dramatically improve efficiency and that the current common practice of keepingp= 1 is a particularly poor choice. For problems with singularities, good efficiency requires that the grid be refined near the points with singularities so theh‐pmethod also requires a grid refinement scheme. We compare two such schemes here which we callE‐Refinement(proposed by Babuska and colleagues recently) andQ‐Refinement(proposed by Rice in the 1960's). Both of these schemes have been shown to have asymptotically optimal order of convergence.The actual behaviours of these two schemes are quite different in practice and the mechanisms for choosing good values ofh, pand the grid refinement parameters are also quite different. This paper presents the results of a systematic experimental study of these two methods and discusses the difficulty of choosing highly efficienth, pand grid refinement parameters. Our study confirms that these two refinements are of approximately equal efficiency given such good choices. The data suggest that the Q‐Refinement is more efficient but the advantage is not dramatic given the uncertainties inherent in choosing numerical methods for practical applications. We conclude that it is substantially simpler to make good choices for the Q‐Refinement than for the E

ISSN:0029-5981    

DOI:10.1002/nme.1620330104

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA two parameter family of incrementally objective integration schemes is proposed for the analysis of a broad range of unified rate‐dependent viscoplastic constitutive models in large deformation problems. A similar scheme can be applied to rate‐independent solids as well. These algorithms are a generalization of the mid‐point integration rule. Full linearization of the principle of virtual work is performed in an updated Lagrangian framework together with a calculation of the consistent linearized moduli. Some details of the finite element implementation are given for plane strain and axisymmetric problems. The method is compared with other objective integration schemes and is tested with several examples where large strains and rotations

ISSN:0029-5981    

DOI:10.1002/nme.1620330105

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA simple and accurate non‐layered plastic element which is capable of capturing the development of plastic curvatures across the thickness of the plates is presented in this paper. The influence of transverse shear forces on the plastic behaviour of plates is also investigated here. This non‐layered plastic element is based on: (i) the four‐node quadrilateral strain element for shear flexible elastic plates given by the authors; (ii) the plastic hinge formulation outlined by Shi and Atluri; and (iii) the modified Ilyushin's yield function which can account for both the development of plastic deformations across the thickness of plates and the effect of transverse shear forces. The numerical examples given here demonstrate that the present non‐layered plastic element can achieve the results obtained by the layered element model and the transverse shear forces considerably affect the plastic behaviour of plates under certain load con

ISSN:0029-5981    

DOI:10.1002/nme.1620330106

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractIn the formulation of a large strain problem, the Euler–Cauchy–Stokes decomposition and the Eulerian objective stress and strain rates used for the formulation of the problem are actually applicable only for some special cases and are not suitable for general large strain and rotation rates. In this paper, the limitations and applicabilities of the conventional large strain formulation under various deformation cases will be stud

ISSN:0029-5981    

DOI:10.1002/nme.1620330107

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper considers complex transcendental eigenvalue problems where one is interested in pairs of eigenvalues that are restricted to take real values only. Such eigenvalue problems arise in dynamic stability analysis of non‐conservative physical systems–flutter analysis of aeroelastic systems, to name one example. Some available solution methods are discussed and a new method is presented. Two computational approaches are described for analytical evaluation of the sensitivities of these eigenvalues when they are dependent on other parameters. The algorithms presented are illustrated through examp

ISSN:0029-5981    

DOI:10.1002/nme.1620330108

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA general method to generate assumed stress and strain fields within the context of mixed finite element methods is presented. The assumed fields are constructed in such a way that internal constraints are satisfieda priori. Consequently, the locking behaviour commonly observed in finite element solutions of problems with internal constraints is avoided. To this end, the assumed stress and strain fields are constructed to satisfya priorithe homogeneous part of the equilibrium equations, thus avoiding Fraeijs de Veubeke's limitation principle. Results obtained using the proposed methodology on a nearly incompressible plane strain problem and thin plate application using a shear deformable theory are indicated.

ISSN:0029-5981    

DOI:10.1002/nme.1620330109

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractAn integral equation whose kernel presents logarithmic singularity is numerically solved by the method of arbitrary collocation points (ACP). As a first step a Gaussian quadrature of ordern(hence of polynomial accuracy 2n− 1) is employed for the numerical approximation of the integral. Until now the collocation, which follows, was performed on special points x̄k, determined as roots of appropriate transcedental functions, in order to retain the 2n− 1 degree of polynomial accuracy of the Gaussian quadrature. In this paper an appropriate interpolatory technique is proposed, so thatxkmay be arbitrary and yet the high (2n− 1) accuracy of the Gaussian quadrature is re

ISSN:0029-5981    

DOI:10.1002/nme.1620330110

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA rank‐sufficient flat triangular shell element with drilling degrees‐of‐freedom is described. A variational basis for this element has been provided by a three‐field variational principle with relaxed interelement compatibility and traction continuity conditions. A generalized spurious mode control procedure has been developed in order to stabilize zero energy kinematical modes. Excellent performance has been found in an obstacle course and buckling p

ISSN:0029-5981    

DOI:10.1002/nme.1620330111

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY