摘要:

AbstractThis investigation concerns itself with the dynamic analysis of thin, laminated composite plates consisting of layers of orthotropic laminae that undergo large arbitrary rigid body displacements and small elastic deformations. A non‐linear finite element formulation is developed which utilizes the assumption that the bonds between the laminae are infinitesimally thin and shear non‐deformable. Using the expressions for the kinetic and strain energies, the lamina mass and stiffness matrices are identified. The non‐linear mass matrix of the lamina is expressed in terms of a set of invariants that depend on the assumed displacement field. By summing the kinetic and strain energies of the laminae of an element, the element mass and stiffness matrix can be defined in terms of the set of element invariants. It is shown that the element invariants can be expressed explicitly in terms of the invariants of its laminae. By assembling the finite elements of the deformable body, the body invariants can be identified and expressed explicitly in terms of the invariants of the laminae of its elements. In the dynamic formulation presented in this paper, the shape functions of the laminae are assumed to have rigid body modes that need to describe only large rigid body translations. The computer implementation and the use of the formulation developed in this investigation in multibody dynamics are discussed in the second part of this

ISSN:0029-5981    

DOI:10.1002/nme.1620360102

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis investigation concerns itself with the computer implementation of the dynamic formulation of thin laminated composite plates consisting of layers of orthotropic laminae that undergo large arbitrary rigid body displacements and small elastic deformations. A finite element preprocessor computer program is developed to automatically generate the invariants of the laminae, which may have arbitrary orientations. The laminae invariants are then used to obtain the invariants of the elements and the composite laminated plate. Theconsistent and lumpedmass formulations of the invariants of motion of composite plates are compared and it is concluded that the two methods are comparable, if a fine enough finite element mesh is used. The structure of the dynamic equations of motion, based on the formulation presented in Part I of this paper, is examined. Non‐linear centrifugal and Coriolis forces arising as the result of the finite rotations of the laminae are defined, and the solution schemes of the resulting non‐linear differential equations of motion are discussed. Numerical examples illustrating the differences between homogeneous isotropic and laminated composite plates are presented. An RSSR (Revolute‐Spherical‐Spherical‐Revolute) mechanism is used in the numerical examples, with the coupler modelled as a laminated plate flexible body. It is found that the inertia of the plate contributed greatly to the transverse deformation. The effects of laminae orientation is also inv

ISSN:0029-5981    

DOI:10.1002/nme.1620360103

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractEigenmode analyses of the element stiffness matrices have been used to assess the impact of the applied integration scheme on the stress predictions of two‐ and three‐dimensional plane interface elements. It is demonstrated that large stress gradients over the element and coupling of the individual node‐sets of the interface element may result in an oscillatory type of response. For line elements and linear plane interface elements the performance can be improved by using either a nodal lumping scheme or Newton‐Cotes or Lobatto integration schemes instead of the more traditional Gauss scheme. For quadratic interface elements the same holds true except for a nodal lumping

ISSN:0029-5981    

DOI:10.1002/nme.1620360104

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper presents the formulation and the numerical implementation of a three‐dimensional direct boundary element method for the Biot theory of poroelasticity. To avoid the need of time‐stepping and volume integration, the solution is performed in the Laplace transform space. Solution in time is obtained via numerical inversion. Several examples, including the settlement of a rectangular footing and a modified Mandel problem, are exami

ISSN:0029-5981    

DOI:10.1002/nme.1620360105

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper presents a hybrid variational method to minimize computational effort in forming and solving the equations of motion for broad classes of rigid multibody mechanical systems. The hybrid method combines theO(n)andO(n3)recursive variational methods for forming the equations of motion in terms of joint relative co‐ordinates. While theO(n3)method is more efficient than theO(n)method for systems with short chains and decoupled loops, the converse is true when the number of bodies in chains is large. The computational complexity of theO(n3)andO(n)methods in forming and solving the equations of motion is analysed as a function of the numbers of bodies, decoupled loops, joints, cut joints, cut‐joint constraint equations and force elements. Based on complexity estimates, the method presented in this paper uses either theO(n)orO(n3)variational method to formulate the equations of motion for each open chain and decoupled loop in the system, to minimize the computational eff

ISSN:0029-5981    

DOI:10.1002/nme.1620360106

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper presents ap‐version least‐squares finite element formulation of the convection‐diffusion equation. The second‐order differential equation describing convection‐diffusion is reduced to a series of equivalent first‐order differential equations for which the least‐squares formulation is constructed using the same order of approximation for each of the dependent variables. The hierarchical approximation functions and the nodal variable operators are established by first constructing the one‐dimensional hierarchical approximation functions of orderspξandpηand the corresponding nodal variable operators in ξ and η‐direction and then taking their products. Numerical results are presented and compared with analytical and numerical solutions for a two‐dimensional test problem to demonstrate the accuracy and the convergence characteristics of the present formulation.The Gaussian quadrature rule used to calculate the numerical values of the element matrices, vectors as well as the error functionalI(E), is established based on the highest degree of the polynomial in the integrands. It is demonstrated that this quadrature rule with the presentp‐version formulation produces excellent results for very low as well as extremely high Peclet numbers (10‐106) and, furthermore, the error functionalI(sum of the integrals ofE2) is a monotonically decreasing function of the number of degrees of freedom as thep‐levels are increased for a fixed mesh. It is shown that exact integration with theh‐version (linear and parabolic elements) produces inaccurate solutions at high Peclet numbers. Results are also presented using reduced integration. It is shown that the reduced integration withp‐version produces accurate values of the primary variable even for relatively lowp‐levels but the error functionalI(when calculated using the proper integration rule) has a much higher value (due to errors in the derivatives of the primary variable) and is a non‐monotonic function of the degrees of freedom asp‐levels are increased for a fixed mesh. Similar behaviour of the error functionalIis also observed for theh‐models using linear elements when reduced integration is used. Although theh‐models using parabolic elements produce monotonic error functional behaviour as the number of degrees of freedom are increased, the error values are inferior to t

ISSN:0029-5981    

DOI:10.1002/nme.1620360107

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620360108

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe coupled thermomechanical responses of fluid‐saturated porous continua subjected to finite deformation are investigated. Field equations governing the transient response of the media are derived from a continuum thermodynamics mixture theory based on mass balance, momentum balance and energy balance laws as well as the Clausius‐Duhem inequality. Finite element procedures for the two‐dimensional response, employing updated Lagrangian formulations for the solid skeleton deformation and the weak formulations for fluid and thermal transport equations, are implemented in a fully implicit form. Temperature‐dependent mechanical properties for the non‐linear solid matrix, characterized by Perzyna's viscoplastic model, are assumed. An iterative scheme based on the full Newton‐Raphson method is presented for simultaneously solving the coupled non‐lin

ISSN:0029-5981    

DOI:10.1002/nme.1620360109

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractA set of field equations, the associated finite element model formulations and numerical methodology for thermomechanical response evaluations of fluid‐saturated media under finite deformation have been presented in Part I of the companion manuscript.1In this paper, the formulations and methodologies are initially validated through benchmark model comparisons prior to constitutive model sensitivity analysis and subsequent thermomechanical response determination. The responses for the testbed problems, using the developed solution algorithm, compare favourably with the reported results. The response investigations for complex geomechanical problems illustrate the general applicability of the developed finite element model simulator in predicting the long‐term thermal, pore pressure, displacement and stress responses of fluid‐saturated porous media subjected to thermomechanical loading, as encountered in nuclear waste management scenarios. The presented formulations and numerical procedures can also be used to investigate a wide range of engineering problems involving hygrothermomechanical response predi

ISSN:0029-5981    

DOI:10.1002/nme.1620360110

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620360101

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY