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Marek-jerzy Pindera - One of the best experts on this subject based on the ideXlab platform.

  • The influence of layers with low transverse Stiffness on the contact response of composite half planes
    Composites Science and Technology, 1999
    Co-Authors: Wang Zhang, Wieslaw K. Binienda, Marek-jerzy Pindera
    Abstract:

    A previously developed local-Global Stiffness Matrix methodology for the response of a composite half plane, arbitrarily layered with isotropic, orthotropic or monoclinic plies, to indentation by a rigid parabolic punch is further extended to accommodate the presence of layers with complex eigenvalues (e.g., honeycomb or piezoelectric layers). First, a generalized plane deformation solution for the displacement field in an orthotropic layer or half plane characterized by complex eigenvalues is obtained by using Fourier transforms. A local Stiffness Matrix in the transform domain is subsequently constructed for this class of layers and half planes, which is then assembled into a Global Stiffness Matrix for the entire multi-layered half plane by enforcing continuity conditions along the interfaces. Application of the mixed boundary condition on the top surface of the half plane indented by a rigid punch results in an integral equation for the unknown pressure in the contact region. The integral possesses a divergent kernel which is decomposed into Cauchy-type and regular parts by the use of the asymptotic properties of the local Stiffness Matrix and a relationship between Fourier and finite Hilbert transforms of the contact pressure. The solution of the resulting singular integral equation is obtained by using a collocation technique based on the properties of orthogonal polynomials developed by Erdogan and Gupta. Examples are presented that illustrate the important influence of low transverse properties of layers with complex eigenvalues, such as those exhibited by honeycombs, on the load versus contact length response and contact pressure distributions for half planes containing typical composite materials.

  • Incipient separation between a frictionless flat punch and an anisotropic multilayered half plane
    International Journal of Solids and Structures, 1994
    Co-Authors: Edward E. Urquhart, Marek-jerzy Pindera
    Abstract:

    Abstract A solution to the frictionless contact of rigid flat indenters on arbitrarily layered, anisotropic half planes is obtained using Fourier transforms and the local-Global Stiffness Matrix technique. The local-Global Stiffness Matrix method involves reformulating the problem in terms of interfacial displacements as the basic unknowns, and has been shown to be an efficient method for solving mixed boundary-value problems of laminated media. The contact problem of a rigid punch gives rise to a mixed boundary condition of known displacement gradient and unknown pressure distribution in the contact area. This mixed boundary condition is reduced to a singular integral equation involving the unknown pressure using the asymptotic properties of the Global Stiffness Matrix. A solution for the contact pressure distribution is then obtained from the singular integral equation using a technique provided by Erdogan, which involves the use of orthogonal Chebychev polynomials. The results are employed to determine the boundaries between full and two-region, and full and three-region, contact solution zones in separation parameter spaces that illustrate the effect of geometric and material parameters on the incipient separation between a flat punch and the top layer of a half plane laminated with isotropic, transversely isotropic and monoclinic plies.

  • Local/Global Stiffness Matrix formulation for composite materials and structures
    Composites Engineering, 1991
    Co-Authors: Marek-jerzy Pindera
    Abstract:

    Abstract An efficient algorithm is outlined for solving boundary-value problems involving laminated composite materials and structures that require satisfaction of both continuity of tractions and displacements along common interfaces. The method is based on the systematic construction of a Global Stiffness Matrix for the entire laminated structure in terms of local Stiffness matrices of the individual layers. The local Stiffness Matrix relates the traction components at the upper and lower (or inner and outer) surface of a given layer to the corresponding displacements. The assembly of local Stiffness matrices into a Global Stiffness Matrix is carried out by enforcing continuity conditions along the interfaces which, in effect, leads to reformulation of the problem in terms of interfacial displacements as the basic unknown variables. This, in turn, results in the elimination of certain redundant continuity conditions and thus reduction in the number of simultaneous algebraic equations that need to be solved. An additional advantage of the local/Global Stiffness Matrix formulation is the ease with which certain mixed boundary-value problems can be reduced to singular integral equations of the Fredholm type for the determination of unknown quantities such as the contact pressure in the case of contact problems and the crack-opening displacement in the case of interfacial crack problems.

  • local Global Stiffness Matrix formulation for composite materials and structures
    Composites Engineering, 1991
    Co-Authors: Marek-jerzy Pindera
    Abstract:

    Abstract An efficient algorithm is outlined for solving boundary-value problems involving laminated composite materials and structures that require satisfaction of both continuity of tractions and displacements along common interfaces. The method is based on the systematic construction of a Global Stiffness Matrix for the entire laminated structure in terms of local Stiffness matrices of the individual layers. The local Stiffness Matrix relates the traction components at the upper and lower (or inner and outer) surface of a given layer to the corresponding displacements. The assembly of local Stiffness matrices into a Global Stiffness Matrix is carried out by enforcing continuity conditions along the interfaces which, in effect, leads to reformulation of the problem in terms of interfacial displacements as the basic unknown variables. This, in turn, results in the elimination of certain redundant continuity conditions and thus reduction in the number of simultaneous algebraic equations that need to be solved. An additional advantage of the local/Global Stiffness Matrix formulation is the ease with which certain mixed boundary-value problems can be reduced to singular integral equations of the Fredholm type for the determination of unknown quantities such as the contact pressure in the case of contact problems and the crack-opening displacement in the case of interfacial crack problems.

Li Hua Wang - One of the best experts on this subject based on the ideXlab platform.

  • Transient response of a transversely isotropic multilayered half-space due to a vertical loading
    Applied Mathematical Modelling, 2017
    Co-Authors: Chun Lin Liu, Li Hua Wang
    Abstract:

    Abstract This paper investigates the transient response of a transversely isotropic multilayered half-space under vertical loadings. With the aid of a Laplace–Hankel transform, the Global Stiffness Matrix for a multilayered half-space is acquired by assembling the analytical layer-element of each layer medium. The solutions for the displacements in the time domain are obtained by using the Global Stiffness Matrix equations and a numerical inversion procedure. The accuracy of the proposed method is verified through comparisons with existing solutions for displacements induced by a step and rectangular pulse loading. In addition, selected numerical results for displacements induced by the buried loading are presented to illustrate the effect of transient loading type and material anisotropy on the transient response.

Nai Rui Cang - One of the best experts on this subject based on the ideXlab platform.

  • Analytical layer element solutions for deformations of transversely isotropic multilayered elastic media under nonaxisymmetric loading
    International Journal for Numerical and Analytical Methods in Geomechanics, 2014
    Co-Authors: Dong Liang Feng, Nai Rui Cang
    Abstract:

    SUMMARY This paper presents the analytical layer element solutions for deformations of transversely isotropic elastic media subjected to nonaxisymmetric loading at an arbitrary depth. The state vectors for the nonaxisymmetric problem are deduced through the substitution of the Hu Hai-chang solutions into the basic equations for the transversely isotropic elastic media. From the state vectors, the analytical layer element of a single layer is obtained in the Hankel transformed domain. The analytical layer element is an exact and symmetric Stiffness Matrix whose elements are without positive exponential functions, which can not only simplify the calculation but also improve the stability of computation. On the basis of the continuity conditions between adjacent layers, the Global Stiffness Matrix is obtained by assembling the interrelated layer elements. The solutions for the multilayered elastic media in the transformed domain are obtained by solving the algebraic equation of the Global Stiffness Matrix, which satisfies the boundary conditions. The actual solutions in the physical domain are further obtained by inverting the Hankel transform. Finally, some cases are analyzed to verify the solutions and evaluate the influences of the transversely isotropic character and stratified character of the media on the load–displacement responses. The numerical results show that the variations of the elastic properties between layers have a great effect on the displacements of the multilayered media. Copyright © 2014 John Wiley & Sons, Ltd.

  • Analytical layer-element solution to axisymmetric dynamic response of transversely isotropic multilayered half-space
    Soil Dynamics and Earthquake Engineering, 2014
    Co-Authors: Nai Rui Cang
    Abstract:

    Abstract Starting with the governing equations of motion and the constitutive equations of transversely isotropic elastic body, and based on the corresponding algebraic operations and the Hankel transform, the analytical layer-elements of a finite layer and a half-space are obtained in the transformed domain. According to the continuity conditions between adjacent layers, the Global Stiffness Matrix equation is obtained by assembling the analytical layer-element of each single layer. The solutions in the transformed domain are acquired by introducing the boundary conditions into the Global Stiffness Matrix equation, and thus, the corresponding solutions in frequency domain are achieved by taking the inversion of Hankel transform. Finally, some numerical examples are given to illustrate the accuracy of the proposed method, and to study the influence of properties and the frequency of excitation on the dynamic response of the medium.

  • Non-axisymmetric Biot consolidation analysis of multi-layered saturated poroelastic materials with anisotropic permeability
    Soils and Foundations, 2013
    Co-Authors: Nai Rui Cang
    Abstract:

    Abstract To start with, an analytical layer-element (i.e., a symmetric Stiffness Matrix), which describes the relationship between the generalized displacements and the stress levels of a layer subjected to non-axisymmetric loading, is exactly derived in the transformed domain by the application of a Laplace–Hankel transform with respect to variables t and r , a Fourier expansion with respect to variable θ , and a Laplace transform and its inversion with respect to variable z , based on the governing equations of Biot’s consolidation of multi-layered saturated poroelastic materials with anisotropic permeability. The analytical layer-element experiences considerable improvement in computation efficiency and stability, since it only contains negative exponential functions in its elements. In addition, a Global Stiffness Matrix for multi-layered saturated poroelastic media is obtained by assembling the interrelated layer-elements based on the continuity conditions between adjacent layers. By introducing the boundary conditions and solving the Global Stiffness Matrix, the solutions in the Laplace–Hankel transformed domain are obtained, and the final solutions can be recovered by a numerical inversion of the Laplace–Hankel transform. Finally, numerical examples are presented to verify the theory and to study the effect of the property of anisotropic permeability on vertical displacements and excess pore pressure. The calculation results show that the property of anisotropic permeability has a great influence on the process of consolidation.

  • Analytical layer-element solutions for a multi-layered transversely isotropic elastic medium subjected to axisymmetric loading
    Journal of Zhejiang University SCIENCE A, 2012
    Co-Authors: Nai Rui Cang, Jie Han
    Abstract:

    This paper presents an analytical layer-element method used to analyze the displacement of a multi-layered transversely isotropic elastic medium of arbitrary depth subjected to axisymmetric loading. Based on the basic constitutive equations and the HU Hai-chang’s solutions for transversely isotropic elastic media, the state vectors of a multi-layered transversely isotropic medium were deduced. From the state vectors, an analytical layer element for a single layer (i.e., a symmetric and exact Stiffness Matrix) was acquired in the Hankel transformed domain, which not only simplified the calculation but also improved the numerical efficiency and stability due to the absence of positive exponential functions. The Global Stiffness Matrix was obtained by assembling the interrelated layer elements based on the principle of the finite layer method. By solving the algebraic equations of the Global Stiffness Matrix which satisfy the boundary conditions, the solutions for multi-layered transversely isotropic media in the Hankel transformed domain were obtained. The actual solutions of this problem in the physical domain were acquired by inverting the Hankel transform. This paper presents numerical examples to verify the proposed solutions and investigate the influence of the properties of the multi-layered medium on the load-displacement response.

Chun Lin Liu - One of the best experts on this subject based on the ideXlab platform.

  • Transient response of a transversely isotropic multilayered half-space due to a vertical loading
    Applied Mathematical Modelling, 2017
    Co-Authors: Chun Lin Liu, Li Hua Wang
    Abstract:

    Abstract This paper investigates the transient response of a transversely isotropic multilayered half-space under vertical loadings. With the aid of a Laplace–Hankel transform, the Global Stiffness Matrix for a multilayered half-space is acquired by assembling the analytical layer-element of each layer medium. The solutions for the displacements in the time domain are obtained by using the Global Stiffness Matrix equations and a numerical inversion procedure. The accuracy of the proposed method is verified through comparisons with existing solutions for displacements induced by a step and rectangular pulse loading. In addition, selected numerical results for displacements induced by the buried loading are presented to illustrate the effect of transient loading type and material anisotropy on the transient response.

M. Shinozuka - One of the best experts on this subject based on the ideXlab platform.

  • New formulation of FEM for deterministic and stochastic beams through generalization of Fuchs' approach
    Computer Methods in Applied Mechanics and Engineering, 1997
    Co-Authors: I. Elishakoff, Y.j. Ren, M. Shinozuka
    Abstract:

    This paper proposes an alternative way of constructing the Global Stiffness Matrix of the finite element method for bending beams, it also applies the new formulation to first and second moment analysis of stochastic beams, which involve spatially uncertain bending Stiffness. Originating from Fuchs' idea of decoupling the shear and bending components in the bending beam, the element level Stiffness Matrix is diagonalized. The generalized stress-strain, strain-displacement and equilibrium relationships are assembled, respectively, and then are combined to form the Global Stiffness Matrix. The advantage of the new formulation is that the bending Stiffness explicitly appears in the Global Stiffness Matrix. The mean vector and covariance Matrix of the displacement of the beam are then obtained in terms of probabilistic characteristics of the uncertain bending Stiffness. This is in contrast to the conventional finite element method in stochastic setting, which is based on the perturbation technique. The example is given to illustrate the efficacy of the new formulation and its application to bending of stochastic beams.

  • Non-Perturbative Fem for Deterministic and Stochastic Beams Through Inverse of Stiffness Matrix
    IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics, 1996
    Co-Authors: I. Elishakoff, Y.j. Ren, M. Shinozuka
    Abstract:

    This paper proposes an alternative way of constructing the Global Stiffness Matrix in the finite element analysis of bending beams, which involve spatially deterministic or stochastical bending Stiffness. Originating from Fuchs’ idea of decoupling the shear and bending components in the bending beam, the element level Stiffness Matrix is diagonalized. The generalized stress-strain, strain-displacement and equilibrium relationships are assembled, respectively, and then are combined to form the Global Stiffness Matrix. The advantage of the new formulation is that the bending Stiffness explicitly appears in the Global Stiffness Matrix, which can be inverted exactly without application of perturbation based expansion. The mean vector and correlation Matrix of the displacement of the beam are then obtained in terms of probabilistic characteristics of the uncertain bending Stiffness. The example is given to illustrate the efficacy of the new formulation and its application to bending of stochastic beams.