摘要:

AbstractWithin the framework of the finite element method an application of the logarithmic strain space formulation of large strain elastoplasticity is illustrated for the examples of axisymmetric three‐node triangular and four‐node quadrilateral finite elements. The formulation of the large strain elastoplasticity is based on a strain space formulation in conjunction with logarithmic (or Hencky) strain tensors with respect to the reference configuration. It is therefore—from a material point of view—a full Lagrangian formulation. The use of logarithmic strains enables an additive split of finite dilatation and distortion, which are given by the logarithmic strain trace and deviator. As a consequence of the strain space formulation no stress tensors are involved in order to describe the plasticity. The stress which is work‐conjugate to the logarithmic strain follows from the stress‐strain relations and may be transformed to Cauchy stress. The desired finite element matrices are derived via the principle of virtual work applied to the Cauchy stress distribution of the current configuration. It should be noted that our considerations are not restricted to axisymmetry and that they remain valid for isoparametric, position‐ (displacement‐) based finite elem

ISSN:0029-5981    

DOI:10.1002/nme.1620381402

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe present paper extends the finite element perturbation approach already presented for pin‐jointed and framed structures15to rectangular thin plates. Koiter's asymptotic strategy2is coupled with aHigh‐Continuityfinite element discretization of the plate.22The consistency of the discrete model is discussed from the kinematical and numerical points of view and several numerical tests are reported. It appears that use of the HC elements makes the perturbation algorithm insensitive to the locking phenomenon occurring in the evaluation of the postbuckling behaviour. It also allows the use of very fine discretization meshes at low computational c

ISSN:0029-5981    

DOI:10.1002/nme.1620381403

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe problem of wave scattering by a plane crack is solved, either in the case of acoustic waves or in the case of elastic waves incidence using the boundary integral equation method. A collocation method is often used to solve that equation, but here we will use a variational method, first writing the problem of Fourier variables, and then writing the associated integrals in the sesquilinear form with weak singularity kernels. This representation is used in the numerical approach, made with a finite element method in the surface of the crack. Numerical tests were made with circular and elliptical cracks, but this method can be extended to other shapes, with the same convergence profiles. Extensive results are given concerning the crack opening displacement, the scattering cross‐section, the back‐scattered amplitude and far‐field pat

ISSN:0029-5981    

DOI:10.1002/nme.1620381404

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe strategy in the boundary element method for the analysis of symmetric domains that does not require the modelling of contours corresponding to the axes of symmetry is investigated for a number of advanced applications. These applications include: treatment of domain loadings, two‐dimensional time domain transient elastodynamics, and the analysis of probabilistic problems in elastostatics with a random geometric configuration. Both symmetric as well as arbitrary loadings acting on the symmetric objects are considered. A number of case studies are presented to provide comparisons of computer memory and CPU time requirements for the analyses of the entire object versus the analyses of only the symmetric portion of the object. The numerical data presented clearly demonstrates the advantages of developing efficient symmetric formulations for advanced application

ISSN:0029-5981    

DOI:10.1002/nme.1620381405

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractStraight and curved cracks are modelled by direct formulation boundary elements, of geometry defined by Hermitian cubic shape functions. Displacement and traction are interpolated by the Hermitian functions, supplemented by singular functions which multiply stress intensity factors corresponding to the dominant modes of crack opening in which displacement is proportional to the square root of distancerfrom the crack tip, and subdominant modes in which it is proportional tor1·5. The singular functions extend over many boundary elements on each crack face.A nodal collocation scheme is used, in which additional boundary integral equations are obtained by differentiation of the equation obtained from Betti's theorem. The hypersingular kernels of the equations so derived are integrated by consideration of trial displacement fields of subdomains lying to either side of the crack. Examples are shown of the analysis of buried and edge cracks, to demonstrate the effects of modelling subdominant modes and extending singular shape functions over many elements

ISSN:0029-5981    

DOI:10.1002/nme.1620381406

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThis paper proposed a new efficient method, the consistent DXDR method, for analysing general elastic‐plastic problems. Two important factors in computational plasticity, the convergence and stability, were addressed. The method was constructed through a natural combination of two vital components: the DXDR algorithm which had been proved to be a powerful equation solver developed by the authors and a stable consistent algorithm for the integration of the constitutive equations of plasticity. Numerical examples demonstrated in detail the efficiency, accuracy, and stability attainable in solving various engineering problem

ISSN:0029-5981    

DOI:10.1002/nme.1620381407

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe method of finite‐part (Hadamard‐type or hypersingular) integrals is already a standard approach in applied numerical methods in engineering and, mainly, in acoustics, fluid dynamics, elasticity and fracture mechanics. Here we study the convergence of the non‐classical (possessing a negative node, outside the integration interval, as well as a negative weight corresponding to this node) Gauss‐Legendre quadrature rule for finite‐part integrals on the interval [0,1] with the weight function 1/y and we prove its validity for integrands possessing a continuous first derivative. The case of integrands possessing a higher‐order derivative is also considered and the rate of convergence is established. These results are based on the derivation of a bound for the negative node in the above quadrature rule and, further, on the theory of convergence of the classical Gauss quadrature rule. Numerical results, verifying the results of this paper, are also displayed. The present results can be generalized to the Gauss‐Laguerre similarly non‐classical quadrature rule for finite‐part integrals (on the interval [0], ∞)) as well as to the two special, but important in engineering applications, non‐classical Gaussian quadrature rules for Cauchy‐type principal‐value integrals and Mangler‐type finite‐part integrals have been propo

ISSN:0029-5981    

DOI:10.1002/nme.1620381408

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA new formulation of a 16‐degree‐of‐freedom conforming quadrilateral plate bending element using the Cartesian co‐ordinates is presented. The displacement functionwis taken as a slight modification of bicubic polynomial in the Cartesian co‐ordinates. Use of this expression in the construction of finite element representations is expected to be useful specially for microcomputers. The simple stiffness matrix subroutine, coded in FORTRAN 77, for the general quadrilateral plate bending element is listed in the

ISSN:0029-5981    

DOI:10.1002/nme.1620381409

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA versatile hybrid finite element scheme consisting of special crack‐tip elements and crack face contact elements is developed to analyse a partially closed interface crack between two dissimilar anisotropic elastic materials. The crack‐tip element incorporates higher‐order asymptotic solutions for an interfacial crack tip. These solutions are obtained from complex variable methods in Stroh formalism. For a closed interfacial crack tip, a generalized contact model in which the crack‐tip oscillation is eliminated is adopted in the calculation. The hybrid finite element modelling allows the stress singularity at an open and closed crack tip to be accurately treated. The accuracy and convergence of the developed scheme are tested with respect to the known interface crack solutions. Utilizing this numerical scheme, the stress intensity factors and contact zone are calculated for a finite interface crack between a laminated composite m

ISSN:0029-5981    

DOI:10.1002/nme.1620381410

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620381412

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY