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1.
The buckling analysis of cross-ply laminated square plates subjected to three types of in-plane forces and various edge boundary conditions is presented on the basis of a unified five-degree-of-freedom shear deformable plate theory. The employment of the appropriate “shear deformation shape functions” in the theory leads to certain shear deformable plate theories developed previously, also, fulfills the requirement of the continuity conditions among the layers. The governing equations of buckling behaviour of completely simply supported cross-ply laminated plates are solved analytically. For the plates with different combinations of free, clamped and simply supported boundary conditions at their edges, the Ritz method is applied by assuming the displacement components as the double series of simple algebraic polynomials. The numerical results obtained on the basis of various plate theories for uniaxial, biaxial compression and compression–tension types of loading and different length-to-thickness ratios are presented and compared with the ones available in the literature. 相似文献
2.
The paper deals with the formulation and implementation of a new symmetric boundary element model for the analysis of Kirchhoff plates. The transversal displacement and normal slope boundary integral equations, usually adopted in the standard boundary element analysis, are considered together with bending moment, twisting moment and equivalent shear boundary integral equations. These equations are weighted by considering distributed sources related to the kinematic and static variables in the virtual-work sense. Moreover, particular attention is paid to the discretization of the boundary variables by shape functions selected in order to ensure continuity over the boundary and symmetry for the matrix system. The evaluation of the highly singular boundary integrals for overlapped integration domains is performed in closed form using a limit approach which provides self-contributions as limit values of non-singular terms. The corner effects and their treatment in the numerical procedure are also discussed. Various numerical examples for plates having different boundary conditions illustrate the performance of the model. 相似文献
3.
Recent developments in the symmetric boundary element method (SBEM) have shown a clear superiority of this formulation over
the collocation method. Its competitiveness has been tested in comparison to the finite element method (FEM) and is manifested
in several engineering problems in which internal boundaries are present, i.e. those in which the body shows a jump in the
physical characteristics of the material and in which an appropriate study of the response must be used. When we work in the
ambit of the SBE formulation, the body is subdivided into macroelements characterized by some relations which link the interface
boundary unknowns to the external actions. These relations, valid for each macroelement and characterized by symmetric matricial
operators, are similar in type to those obtainable for the FEM. The assembly of the macroelements based on the equilibrium
conditions, or on the compatibility conditions, or on both of these conditions leads to three analysis methods: displacement,
force, and mixed-value methods, respectively. The use of the fundamental solutions involves the punctual satisfaction of the
compatibility and of the equilibrium inside each macroelement and it causes a stringent elastic response close to the actual
solution. Some examples make it possible to perform numerical checks in comparison with solutions obtainable in closed form.
These checks show that the numerical solutions are floating ones when the macroelement geometry obtained by subdividing the
body changes.
Received 26 January 2001 相似文献
4.
5.
Ahmed K. Noor Jeanne M. Peters 《International journal for numerical methods in engineering》1987,24(11):2057-2070
An officient preconditioned conjugate gradient (PCG) technique and a computational procedure are presented for the analysis of symmetric anisotropic structures. The technique is based on selecting the preconditioning matrix as the orthotropic part of the global stiffness matrix of the structure, with all the nonorthotropic terms set equal to zero. This particular choice of the preconditioning matrix results in reducing the size of the analysis model of the anisotropic structure to that of the corresponding orthotropic structure. The similarities between the proposed PCG technique and a reduction technique previously presented by the authors are identified and exploited to generate from the PCG technique direct measures for the sensitivity of the different response quantities to the non-orthotropic (anisotropic) material coefficients of the structure. The effectiveness of the PCG technique is demonstrated by means of a numerical example of an anisotropic cylindrical panel. 相似文献
6.
B. S. Shul'ginov 《Strength of Materials》1995,27(11-12):680-687
The influence of low temperature on the reliability of machine parts and on the characteristics of strength of steels and their weld joints is analyzed. It is established that a drop in temperature in impact cyclic loading causes a decrease in fatigue resistance of weld joints of low-alloy steels and a corresponding increase in relative frequency of crack formation in them. A comparison of experimental and service data shows that the increase in service relative frequency of crack formation in welded machine parts at reduced temperature is an indication of their fatigue origin. It was concluded that the increase in the frequency of failures of welded machine parts with a reduction in temperature observed under service conditions is caused by a reduction in their fatigue resistance and an increase in the tendency of their materials toward brittle fracture. 相似文献
7.
In this paper, oscillators with asymmetric and symmetric quadratic nonlinearity are compared. Both oscillators are modeled as ordinary second-order differential equations with strong quadratic nonlinearities: one with positive quadratic term and the second with a quadratic term which changes the sign. Solutions for both equations are obtained in the form of Jacobi elliptic functions. For the asymmetric oscillator, conditions for the periodic motion are determined, while for the symmetric oscillator a new approximate solution procedure based on averaging is developed. Obtained results are tested on an optomechanical system where the motion of a cantilever in the intracavity field is oscillatory. Two types of quadratic nonlinearities in the system are investigated: symmetric and asymmetric. The advantage and disadvantage of both models is discussed. The analytical procedure suggested in the paper is applied. The obtained solution agrees well with a numerical one. 相似文献
8.
In the context of linear elasticity, this paper presents a way to perform hypersingular integrals arising from the symmetric
Galerkin Boundary Element Method (BEM). In contrast to the existing integration techniques, the one here proposed does not
need any regularization or limit processes: in fact it works directly on the final form of the hypersingular double integrals
without any previous manipulation. The present method is applied to 2D linear elastic problems, using straight elements with
continuous piecewise-linear displacements and piecewise-constant tractions. Numerical tests are presented for the validation
of the obtained analytic results. 相似文献
9.
P. Balasubramanian J. G. Jagadeesh H. K. Suhas V. Ramamurti 《International journal for numerical methods in engineering》1993,36(2):273-285
In this study the free vibration of circumferentially periodic structures has been analysed using the block Lanczos method in a semi complex domain for extracting real natural frequencies and complex mode shapes. The influence of the number of vectors in the block and also the effect of renumbering of nodes, depending on whether they are internal, adjacent or boundary nodes, on the CPU time are studied. The efficiency of the present method is compared with the subspace iteration schemes. 相似文献
10.
Joan Baiges Ramon Codina Florian Henke Shadan Shahmiri Wolfgang A. Wall 《International journal for numerical methods in engineering》2012,90(5):636-658
In this paper, we propose a way to weakly prescribe Dirichlet boundary conditions in embedded finite element meshes. The key feature of the method is that the algorithmic parameter of the formulation which allows to ensure stability is independent of the numerical approximation, relatively small, and can be fixed a priori. Moreover, the formulation is symmetric for symmetric problems. An additional element-discontinuous stress field is used to enforce the boundary conditions in the Poisson problem. Additional terms are required in order to guarantee stability in the convection–diffusion equation and the Stokes problem. The proposed method is then easily extended to the transient Navier–Stokes equations. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
11.
The allowance for the dependence of the coefficient of thermal conductivity on the temperature and the accuracy of maintenance of the boundary condition in the absolute method of measurement of heat conduction in a quasisteady mode with asymmetric coundary conditions is analyzed by the methods of perturbation theory (iteration method).Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 1, pp. 108–110, July, 1977. 相似文献
12.
Based on the first-order shear deformation beam theory, considering geometric nonlinearity, the governing equations for symmetric laminated composite beams subjected to uniform temperature rise are derived by using Hamilton’s principle, and then three solving methods are presented to deal with it. By introducing an auxiliary function, which is shown in method one, the governing equations are reduced to be a single fourth-order integral-differential equation, and the exact solutions for the thermal buckling and postbuckling of symmetric laminated composite beams with combination of in-plane immovable simply supported and clamped boundary conditions are presented for the first time. On the basis of the results given in the method one, the explicit solutions for the thermal buckling and postbuckling of the beams are presented by giving accurate displacement functions (method two) and Ritz method (method three), respectively. Then, the effects of the transverse shear effects and boundary conditions on the thermal buckling and postbuckling of the beams are qualitatively discussed. What is more, a preliminary discussion on the probability and difference of extending the giving methods to the higher-order shear deformation beam theory with various boundary conditions is conducted. In the numerical examples, the good agreements between the present results and existing solutions verify the validity and efficiency of the present analysis and numerical results. And then the symmetric cross-ply laminated composite beam (0/90/0) is taken as an example to numerically evaluate the effects of the length-to-thickness ratio, beam theories, and boundary conditions on the thermal buckling and postbuckling of symmetric laminated composite beams. Some meaningful conclusions have been drawn. 相似文献
13.
The problem of the transient quasi-static analysis of a poroelastic body subjected to a history of external actions is formulated
in terms of four boundary integral equations, using time-dependent Green's functions of the “free” poroelastic space. Some
of these Green's functions, not available in the literature are derived “ad hoc”. The boundary integral operator constructed
is shown to be symmetric with respect to a time-convolutive bilinear form so that the boundary solution is characterized by
a variational property and its approximation preserving symmetry can be achieved by a Galerkin boundary element procedure.
Communicated by S. N. Atluri, 1 July 1996 相似文献
14.
Abstract The fatigue behavior of a crack in a missile structure is studied using the dual boundary integral equations developed by Hong and Chen (1988). This method, which incorporates two independent boundary integral equations, uses the displacement equation to model one of the crack boundaries and the traction equation to the other. A single domain approach can be performed efficiently. The stress intensity factors are calculated and the paths of crack growth are predicted. In order to evaluate the results of dual BEM, four examples with FEM results are provided. Two practical examples, cracks in a V‐band and a solid propellant motor are studied and are compared with experimental data. Good agreement is found. 相似文献
15.
In this paper, a non-singular boundary element formulation for 3D-elastostatics and 3D-elastodynamics is presented. The proposed method is based on a generalized variational principle. A weighted superposition of static fundamental solutions is used for the field approximation in the domain, whereas the displacement and stress field on the boundary are interpolated by well-known polynomial shape functions. By separating time- and space-dependence a symmetric equation of motion is derived with time-independent mass and stiffness matrix. The domain integral over inertia terms, leading to the mass matrix, is analytically transformed to the boundary. Thus, a boundary only formulation is derived. Comparing numerical results with analytical solutions clearly shows that the obtained system of equations is well-suited for dynamic problems. 相似文献
16.
The steady-state bifurcations near a double-zero eigenvalue of the reaction-diffusion equations associated with a trimolecular chemical reaction (the Brusselator) are analysed for the case of one spatial variable and non-flux boundary conditions. The analysis is based on a previously obtained classification of steady-state mode interactions of codimension two that can occur in non-flux boundary-value problems. All possible codimension-two bifurcations are examined for the coupling of the first two modes. It is also shown that degeneracies of codimension greater than two cannot appear. The structurally stable bifurcation diagrams near a codimension-two bifurcation exhibit a number of non-local phenomena like hysteresis, mode-jumping and bifurcations to time-periodic states. 相似文献
17.
R. Piltner 《Computational Mechanics》1994,15(2):137-160
The classical Trefftz-method can be generalized such that different types of finite elements and boundary elements are obtained. In a Trefftz-type approach we utilize functions which a priori satisfy the governing differential equations. In this paper the systematic construction of singular Trefftz-trial functions for elasticity problems is discussed. For convenience a list of solution representations and particular solutions is given which did not appear together elsewhere. The Trefftz-trial functions with singular expressions on the boundary are constructed such that the physical components (stresses, strains, displacements) remain finite in the solution domain and on the boundary. The unknown coefficients of the linearly independent Trefftz-trial functions for the physical components can be obtained by using a variational formulation. The symmetric coefficient matrix in the discussed procedure can be obtained from the evaluation of boundary integrals. As an application of the proposed boundary element algorithm, the symmetric stiffness matrices of subdomains (finite element domains) are calculated. For the numerical example the solution domain is decomposed into triangular subdomains so that a standard finite element program could be used to assemble the system of equations. The chosen example is meant as a simple test for the proposed algorithm and should not be understood as a proposal for a new triangular finite element. Using the proposed boundary element techniques, symmetric stiffness matrices for irregular shaped subdomains (finite elements) can be derived. However, in order to use the method in a finite element package for the coupling of irregular shaped subdomains some program modifications will be necessary. 相似文献
18.
The Galerkin and collocation methods are combined in the implementation of a boundary integral formulation based on the Trefftz
method for linear elastostatics. A finite element approach is used in the derivation of the formulation. The domain is subdivided
in regions or elements, which need not be bounded, simply connected or convex. The stress field is directly approximated in
each element using a complete solution set of the governing Beltrami condition. This stress basis is used to enforce on average,
in the Galerkin sense, the compatibility and elasticity conditions. The boundary of each element is, in turn, subdivided into
boundary elements whereon the displacements are independently approximated using Dirac functions. This basis is used to enforce
by collocation the static admissibility conditions, which reduce to the Neumann conditions as the stress approximation satisfies
locally the domain equilibrium condition. The resulting solving system is symmetric and sparse. The coefficients of the structural
matrices and vectors are defined either by regular boundary integral expressions or determined by direct collocation of the
trial functions. 相似文献
19.
The main objective of this article is to develop a methodology for the efficient calculation of buckling loads for frame structures having high-order symmetry properties in order to reduce the size of their associated eigenvalue problems. This is achieved by decomposing the second-order stiffness matrix of a symmetric model into submatrices using a representation of its symmetry group, via a step-by-step approach. The physical interpretation of the resulting submatrices is shown as substructures (factors), and the possibility of further decomposition is then investigated for each of the constructed submodels. Due to the similarity in transformation, the constructed submatrices contain the eigenvalues of the main structural matrix. The buckling load of the entire structure is obtained by calculating the buckling loads of its factors. The methods of the present paper provide a mathematical foundation and a logical means to deal with symmetry instead of looking for various boundary conditions to be imposed for symmetric structures, as in the traditional methods. Examples are provided to illustrate the simplicity and efficiency of the present method. 相似文献
20.
A. A. Elizarov 《Measurement Techniques》1999,42(1):61-65
Discussed are the specific features of thin-film magnetodielectric, dynamic radio-wave sensitive elements for instrumental
transducers whose properties are described by tensors of surface permittivity and permeability. It is shown that their calculation
and simulation is considerably simplified by the introduction of equivalent boundary conditions (averaging of magnetic fields
over the structure thickness).
Translated from Izmeritel'naya Tekhnika, No. 1, pp. 42–45, January, 1999. 相似文献