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Showing papers on "Linear elasticity published in 1989"



Journal ArticleDOI
TL;DR: In this article, the adhesive joint is modelled as an adherend-adhesive sandwich with any combination of tensile, shear and moment loading being applied at the ends of both adherends.

253 citations


Journal ArticleDOI
TL;DR: The motivation of the constitutive equation of the masonry-like material is discussed in this paper. But the motivation is not discussed in this paper, as it is shown in the present paper.
Abstract: The first part of the paper is devoted to the motivation of the constitutive equation of the masonry-like material. It is proved that this equation is the result of three fundamental constitutive assumptions: infinitesimal elasticity, no tensile strength, and a postulate of normality. A necessary and sufficient condition for the existence of a strain energy function is also supplied.

227 citations


Journal ArticleDOI
TL;DR: In this article, the dynamic response of a composite laminate plate to transverse impact loading is simulated numerically and an FEM scheme based on an eight-point brick element and three dimensional linear elasticity theory is employed, assuming that the laminate layers are homogeneous and orthotropic.

178 citations


Journal ArticleDOI
TL;DR: In this paper, a procedure for nonlinear analysis of reinforced concrete membrane structures is described, based on an interative, secant stiffness formulation and employing constitutive relations for concrete and reinforcement based on the modified compression field theory.
Abstract: A procedure is described whereby linear elastic finite element routines can be modified to enable nonlinear analysis of reinforced concrete membrane structures. The proposed procedure is based on an interative, secant stiffness formulation and employs constitutive relations for concrete and reinforcement based on the modified compression field theory. Predictions from the proposed procedure are compared against experimental results, as well as against more complex fourmulations, and excellent accuracy is found. Example analyses and potential applications of the nonlinear procedure are also described.

171 citations



Journal ArticleDOI
TL;DR: In this paper, the constitutive relations describing the fluid pressure response of a porous medium to changes in stress and temperature must reflect the microscopic processes that are operative over the time scale allowed for the deformation.
Abstract: The constitutive relations describing the fluid pressure response of a porous medium to changes in stress and temperature must reflect the microscopic processes that are operative over the time scale allowed for the deformation. Short-duration deformations are readily described by undrained moduli, and intermediate duration deformations by drained moduli, both of which are formulated through linear elastic theory. Long-term deformations that operate over geologic time are normally dominated by irreversible processes and result in considerably larger deformations, for the same applied stress conditions, than would be expected from their elastic counterparts. Model constitutive equations are developed for both elastic and irreversible processes and the magnitude and interpretation of the relevant material properties examined. Although the theory is presented in general terms, a sample calculation shows that for sandstone the inelastic deformation is one and one half orders of magnitude greater than the elastic deformation at the same applied stress. This difference in magnitude has a significant effect on the effective hydraulic diffusivity, various pore pressure coefficients, and the prospective fluid pressure development of the sediment.

113 citations


Journal ArticleDOI
TL;DR: In this article, the uniqueness of the solutions of a class of initial-boundary value problems in linear, isotropic, homogeneous, nonlocal elasticity was proved based on the positive definiteness of total strain energy.

94 citations


Journal ArticleDOI
TL;DR: It is proposed that no single tangent (elastic) modulus from a stress-strain curve of a plant tissue is sufficient to characterize the material properties of a sample and it is suggested that when a modulus is calculated that it be referred to as the tissue composite modulus to distinguish it from the elastic modulus of a noncellular solid material.
Abstract: The mechanical behavior of plant tissues and its dependency on tissue geometry and turgor pressure are analytically dealt with in terms of the theory of cellular solids. A cellular solid is any material whose matter is distributed in the form of beamlike struts or complete "cell" walls. Therefore, its relative density is less than one and typically less than 0.3. Relative density is the ratio of the density of the cellular solid to the density of its constitutive ("cell wall") material. Relative density depends upon cell shape and the density of cell wall material. It largely influences the mechanical behavior of cellular solids. Additional important parameters to mechanical behavior are the elastic modulus of "cell walls" and the magnitude of internal "cell" pressure. Analyses indicate that two "stiffening" agents operate in natural cellular solids (plant tissues): 1) cell wall infrastructure and 2) the hydrostatic influence of the protoplasm within each cellular compartment. The elastic modulus measured from a living tissue sample is the consequence of both agents. Therefore, the mechanical properties of living tissues are dependent upon the magnitude of turgor pressure. High turgor pressure places cell walls into axial tension, reduces the magnitude of cell wall deformations under an applied stress, and hence increases the apparent elastic modulus of the tissue. In the absence of turgid protoplasts or in the case of dead tissues, the cell wall infrastructure will respond as a linear elastic, nonlinear elastic, or "densifying" material (under compression) dependent upon the magnitude of externally applied stress. Accordingly, it is proposed that no single tangent (elastic) modulus from a stress-strain curve of a plant tissue is sufficient to characterize the material properties of a sample. It is also suggested that when a modulus is calculated that it be referred to as the tissue composite modulus to distinguish it from the elastic modulus of a noncellular solid material. THE MECHANICAL BEHAVIOR of plant tissues varies as a function of turgor pressure and the geometry of their constituent cells. Studies indicate that the elastic modulus of pith parenchyma increases monotonically as turgor pressure increases (Falk, Hertz, and Virgin, 1958; Lin and Pitt, 1986). (The elastic modulus is measured from the slope of the linear portion of a material's stress-strain curve. It measures a specimen's material properties.) A similar relationship has been reported for more anatomically complex structures, such as the leaves of Dubautia and Allium (Robichaux, Holsinger, and Morse, 1986; Niklas and O'Rourke, 1987). In addition to the influence of water content, the elastic modulus of a tissue increases as the ratio of cell wall to protoplasm increases (Niklas, 1989a), while the maximum elastic modulus of algal and higher plant cells decreases as cell size decreases but the cell wall fraction remains relatively constant (Steudle, Zimmermann, and Luttge, 1977; Robichaux I Received for publication 31 May 1988; revision accepted 7 February 1989. et al., 1986). Cell wall composition is another factor that can influence the mechanical properties of tissues. However, data relating to this issue are limited (see Mark, 1967). The influence of turgor pressure and the ratio of cell wall thickness to cell radius on the elastic modulus of pith parenchyma has been modelled by various authors (Nilsson, Hertz, and Falk, 1958; Pitt, 1982, 1984; Gatesetal., 1986; Lin and Pitt, 1986). In all cases, cells are approximated as thin-walled spheres, for which simple shell theory yields the relationship at = Pr/2, where a is the circumferential stress on a cell with a wall-thickness t, radius r, and a turgor pressure of P (see Lin and Pitt, 1986, p. 306). This relationship conforms well to empirical data from pith tissues, since t << r. An underlying assumption to these models is that tissue stiffness increases as the number of cells in a tissue sample increases because increasing cell numbers decrease the capacity for cell-tocell displacements, particularly as turgor pressure increases. This has been experimentally verified (Niklas, 1988). However, for plant tissues other than parenchyma, the assumptions of simple shell theory are violated (cell walls

90 citations


Journal ArticleDOI
TL;DR: In this article, the shear-lag model is applied to a monolayer, unidirectional, fiber-reinforced composite loaded in tension, and the time dependence of the effective load transfer length is calculated.

85 citations


Journal ArticleDOI
TL;DR: In this paper, the authors developed solutions for axisymmetric excavations in infinite media having power law and exponential variations of elastic modulus with minor principal stress and showed that the maximum stress concentrations do not occur at the excavation boundaries and are less than the constant value of 2.0 given by constant modulus elasticity.
Abstract: Porous or clastic rocks often have elastic moduli which are not constant but increase with increasing minor principal stress. The use of classical constant modulus linear elasticity in these cases can lead to erroneous predictions of the deformations and of the initiation and extent of failure around underground excavations. To illustrate these effects, solutions are developed for axisymmetric excavations in infinite media having power law and exponential variations of elastic modulus with minor principal stress. The maximum stress concentrations do not occur at the excavation boundaries and are less than the constant value of 2.0 given by constant modulus elasticity. When modified slightly to allow for test boundary conditions, the theory gives predictions that are consistent with aspects of the results obtained in hydrostatic compression tests on thick walled cylinders of three sedimentary rocks.

Journal ArticleDOI
TL;DR: Results of the Delaunay triangulations to the Voronoi tessellations provide the basis for development of analytical models of various heterogeneous solids, e.g. granular, fibrous.
Abstract: A study is conducted of the influence of microscale geometric and physical randomness on effective moduli of a continuum approximation of disordered microstructures. A particular class of microstructures investigated is that of planar Delaunay networks made up of linear elastic rods connected by joints. Three types of networks are considered: Delaunay networks with random geometry and random spring constants, modified Delaunay networks with random geometry and random spring constants, and regular triangular networks with random spring constants. Using a structural mechanics method, a numerical study is conducted of the first and second order characteristics of random fields of effective moduli. In view of duality of the Delaunay triangulations to the Voronoi tessellations, these results provide the basis for development of analytical models of various heterogeneous solids, e.g. granular, fibrous.

Journal ArticleDOI
Mary E. Morley1
TL;DR: In this paper, a family of finite elements for use in mixed formulations of linear elasticity is developed, where the stresses are not required to be symmetric, but only to satisfy a weaker condition based upon Lagrange multipliers.
Abstract: A family of finite elements for use in mixed formulations of linear elasticity is developed. The stresses are not required to be symmetric, but only to satisfy a weaker condition based upon Lagrange multipliers. This is based on the same formulation used in the PEERS finite element spaces. Elements for both two and three dimensional problems are given. Error analysis on these elements is done, and some superconvergence results are proved.

Journal ArticleDOI
TL;DR: The analysis of a beam-column using stability functions as an alternative to the stress stiffness matrix is discussed in this article, in terms of member length, cross-sectional properties, axial force, and the end moments.
Abstract: Members carrying both axial force and bending moment are subjected to an interaction between these effects. The analysis of a beam-column using stability functions as an alternative to the stress stiffness matrix is discussed. Explicit expressions for stability functions for three-dimensional beam-columns, in terms of member length, cross-sectional properties, axial force, and the end moments, are derived. The effect of flexure on axial stiffness and the effect of axial force on flexural stiffness and stiffness against translation are considered in the derivation of stability functions. The effect of axial force on torsional stiffness and the effect of torsional moment on axial stiffness are neglected. The nonlinear stiffness matrix of a three-dimensional beam-column using the stability functions is presented by modifying the linear elastic stiffness matrix for a beam-column (which includes the effect of shear deformations) available in the literature. A numerical example showing the calculation of stability functions for a given beam-column is also presented.

Journal ArticleDOI
TL;DR: In this article, a one-parameter family of mixed variational principles for linear elasticity is constructed, which includes the generalized Hellinger-Reissner and total potential energy principles as special cases.
Abstract: A one-parameter family of mixed variational principles for linear elasticity is constructed. This family includes the generalized Hellinger-Reissner and total potential energy principles as special cases. The presence of the free parameter offers an opportunity for the systematic derivation of energy-balanced finite elements that combine displacement and stress assumptions. It is shown that Fraeijs de Veubeke's stress-assumption limitation principle takes a particulary elegant expression in terms of the parametrized discrete form. Other possible parametrizations are briefly discussed.

Journal ArticleDOI
TL;DR: In this article, the problem of calculating the boundary and internal conditions on a deformed specimen given approximate information on the displacements at discrete "sensor locations" in the specimen is discussed.
Abstract: This paper is concerned with solution by the boundary element method (BEM) of a certain class of inverse linear elastic problems using the spatial regularization method. More specifically, the problem of calculating the boundary and internal conditions on a deformed specimen given approximate information on the displacements at discrete ‘sensor locations’ in the specimen is discussed. The solution algorithm employs a sensitivity analysis and a least-squares minimization of the difference between the calculated and measured displacements at each sensor location. The ideas presented here can be applied to contact problems where measurements of the deformation at the contact area are difficult.

Journal ArticleDOI
TL;DR: In this paper, a general and simple method is presented for the determination of stress intensity factors in elasticity problems involving several interacting cracks and complex crack shapes using a superposition scheme and an approximation of certain unknown crack-line tractions by a series of base functions.

Journal ArticleDOI
TL;DR: In this paper, a new finite element formulation for elastic-plastic large deflection analysis of shells of revolution is presented, which contains most of the best features of nonlinear finite element analyses currently available in the literature, together with some new numerical schemes to improve the capability, accuracy and speed of the computation.

Journal ArticleDOI
TL;DR: In this article, a macroscopic static theory of gels upon swelling or volume phase transition was developed, and the stability criteria for uniaxially strained bulk gels were derived for spherically symmetric geometry with the outer boundary of the gel having a finite radius.
Abstract: We develop a macroscopic static theory of gels upon swelling or volume phase transition. After deriving the linear elasticity theory of strained systems from the general nonlinear formalism of deformation, we show that the surface modulational instability of a gel plate occurs as the result of softening of (generalized) Rayleigh surface waves. We also derive the stability criteria for uniaxially strained bulk gels. In addition to these linear analyses we developed, for the first time to our knowledge, a theory of three-dimensional phase coexistence of gels exhibiting a volume phase transition. Our study is limited mostly to the case of spherically symmetric geometry with the outer boundary of the gel having a finite radius. Various features of the two phase coexistence are found, some of which have no counterparts in the usual phase separation in binary fluids or gas-liquid systems.

Journal ArticleDOI
TL;DR: In this paper, higher order weight functions for calculating power expansion coefficients of a regular elastic field in a two-dimensional body in the absence of body forces are developed, and the significance of these expansion coefficients in fracture analysis is also discussed.

Journal ArticleDOI
TL;DR: In this paper, a one-parameter family of d-generalized hybrid/mixed variational principles for linear elasticity is constructed following a domain subdivision, which includes the generalised Hellinger-Reissner and potential energy principles as special cases.
Abstract: A one-parameter family of d-generalized hybrid/mixed variational principles for linear elasticity is constructed following a domain subdivision. The family includes the d-generalized Hellinger-Reissner and potential energy principles as special cases. The parametrized principle is discretized by independently varied internal displacements, stresses and boundary displacements. The resulting finite element equations are studied following a physically motivated decomposition of the stress and internal displacement fields. The free formulation of Bergan and Nygard is shown to be a special case of this element type, and is obtained by assuming a constant internal stress field. The parameter appears as a scale factor of the higher-order stiffness.

Journal ArticleDOI
TL;DR: In this paper, the free formulation of Bergan and Nygard has been recast within the framework of a mixed-hybrid functional that allows internal stresses, internal displacements, and boundary displacements to vary independently.
Abstract: The free formulation of Bergan and Nygard has been successfully used in the construction of high-performance finite elements for linear and nonlinear structural analysis. The present paper recasts the free formulation within the framework of a mixed-hybrid functional that allows internal stresses, internal displacements, and boundary displacements to vary independently

01 May 1989
TL;DR: In this article, an articulated structure is defined as an assembly of flexible bodies that may be coupled by kinematic connections and force elements that permit large relative displacement and rotation within flexible bodies.
Abstract: An articulated structure is defined as an assembly of flexible bodies that may be coupled by kinematic connections and force elements that permit large relative displacement and rotation. Kinematics of such systems is defined using one reference frame for each body in the system and deformation modal coordinates that define displacement fields within flexible bodies. Deformation kinematics are defined by both elastic vibration and static correction deformation modes. Linear elastic deformation is presumed; i.e., a linear stress-strain relation is valid and relative displacements within each elastic component are small enough so that the theory of linear elasticity applies. Coupling of reference and modal coordinates leads to a system of nonlinear equations of motion. Methods of automatically generating and solving these equations of motion are outlined.

Journal ArticleDOI
TL;DR: A unified approach for explicit structural design sensitivity analysis of linear elastic systems is presented in this paper, where first-order sensitivity expressions involving the complete set of design variable, including shape design parameters, are derived for general response functional.

Journal ArticleDOI
TL;DR: In this paper, the authors considered the representation of three-dimensional displacement fields in linear elasticity in terms of six complex valued functions, including the complex Muskhelishvili formulation for plane strain as a special case.
Abstract: In this paper the representation of three-dimensional displacement fields in linear elasticity in terms of six complex valued functions is considered. The representation includes the complex Muskhelishvili formulation for plane strain as a special case. The completeness of the complex representation for regular solutions is shown and a relationship to the Neuber/Papkovich solutions is given.

Journal Article
TL;DR: In this paper, the displacement boundary value problems of homogeneous, isotropic, linear, nonlocal elasticity are defined and a Hilbert space is defined and an inequality which plays an important role in the existence theory of elasticity is proven.
Abstract: The displacement boundary value problems of homogeneous, isotropic, linear, nonlocal elasticity are defined. A Hilbert space is defined and an inequality which plays an important role in the existence theory of elasticity is proven. Finally, it is shown that the bilinear form which appears in the weak formulation satisfies the requirements of the fundamental existence lemma (Lax-Milgram's Theorem)

Journal ArticleDOI
TL;DR: In this article, a complete characterization of displacements, bending moments and shear forces of linear elastic beams is given, including a characterization of the stress field of order 0 and of axial and sheer stresses of order 1.
Abstract: This work is a continuation of an earlier work by Bermudez and Viano (1984) on the same subject. In fact, using the same asymptotic expansion in linear elastic beams we give a complete characterization of displacements, bending moments and shear forces of orders 0, 1 and 2. These results include a characterization of the stress field of order 0 and of the axial and shear stresses of order 1. An appropriate physical interpretation of these results, which is considered elsewhere, will allow us to derive and to justify, from a mathematical point of view, the most well-known classical extension, bending and torsion theories for linear elastic beams, including the Bernoulli-Navier, Saint Venant, Timoshenko and Vlasov models.

Journal ArticleDOI
TL;DR: In this paper, a suite of tests employed to determine the accuracy and robustness of shell finite elements for linear elastic and geometric nonlinear problems is presented, with particular emphasis on testing element sensitivity to distortions, validation of spurious zero-energy mode stabilization procedures, and use of linear elastic tests for selection of good nonlinear elements.

Journal ArticleDOI
TL;DR: In this article, the dimensionless load and load-point displacement (u) were introduced to discuss crack propagation problems and the universal −ũ relation for the case of equilibrium crack propagation in any linear elastic material was demonstrated to lie on a single universal fracture curve independent of material.
Abstract: The dimensionless load () and load-point displacement (u) are introduced to discuss crack propagation problems. The −ũ relation for the case of equilibrium crack propagation in any linear elastic material is demonstrated to lie on a single universal fracture curve independent of the material. The concept of the universal −ũ relation is extended to yield a direct and simple form of the dimensionless total energy (eq(α)) which is applicable to many types of instability problems for crack extension, when the shape factor (Y) of the specimen is known as a function of crack length (a). In addition, by applying the deviation of the experimentally observed —ũ curve and the theoretical universal fracture curve, the evaluation of the nonlinear fracture resistance parameter of a polycrystalline graphite material, as an example, was demonstrated.

Journal ArticleDOI
TL;DR: In this article, a method for recovering the gradients of the finite element approximations to a root mean square accuracy of O(h2) was proposed, both at element edge midpoints and element vertices, using simple averaging schemes over adjacent elements.
Abstract: Piecewise linear finite element approximations to two-dimensional Poisson problems are treated. For simplicity, consideration is restricted to problems having Dirichlet boundary conditions and defined on rectangular domains Ω which are partitioned by a uniform triangular mesh. It is also required that the solutions u ∈ H3 (Ω). A method is proposed for recovering the gradients of the finite element approximations to a root mean square accuracy of O(h2), both at element edge mid-points and element vertices, using simple averaging schemes over adjacent elements. Piecewise linear interpolants (respectively discontinuous and continuous) are then fitted to these recovered gradients, and are shown to be O(h2) estimates for ∇u in the L2-norm, and thus superconvergent. A discussion is given of the extension of the results to problems with more general region and mesh geometries, boundary conditions and with solutions of lower regularity, and also to other second-order elliptic boundary value problems, e.g. the problem of planar linear elasticity.