Showing papers on "Linear elasticity published in 1974"

Elasticity in engineering mechanics

Abstract: Introductory Concepts and Mathematics. Theory of Deformation. Theory of Stress. Three--Dimensional Equations of Elasticity. Plane Theory of Elasticity in Rectangular Cartesian Coordinates. Plane Elasticity in Polar Coordinates. Prismatic Bar Subjected to End Load. General Solutions of Elasticity. References. Bibliography. Index.

On the overall moduli of non-linear elastic composite materials

Abstract: F rom the work of R. Hill on constitutive macro-variables it is known that for an inhomogeneous elastic solid under finite strain an overall elastic constitutive law may be defined. In particular, the volume average of the strain energy of the solid is a function only of the volume-averaged deformation gradient. In view of the importance of this result it is re-derived in this paper as a prelude to a discussion of composite materials. A composite material consisting of a dilute suspension of initially spherical inclusions embedded in a matrix of different material is considered. For second-order isotropic elasticity theory an expression for the overall bulk modulus of the composite material is obtained in terms of the moduli of the constituents. When the inclusions are vacuous a known result for the bulk modulus of porous materials is recovered. In certain situations the strengthening/ weakening effects of the inclusions are less pronounced in the second-order theory than in the linear theory.

Transverse Compressive Moduli and Yield Behavior of Some Orthotropic, High-Modulus Filaments

Abstract: An account is given of the experimental determination of the transverse elastic moduli and yield behavior of some commercially available organic and graphite high-modulus filaments. The experimental technique involves transverse compression of single cylindrical filaments between two parallel flat platens and concurrent measurement of the platen- relative displacements and contact forces on the filaments. A theoretical discussion of the transverse compressional behavior of a linear elastic, homogeneous, orthotropic cylinder is presented. Using the theoretical results and the trans verse load-displacement measurements, a technique is developed for calculating the elastic moduli and maximum shear stresses at yield or fracture.

Nonlocal Elasticity and Waves

Abstract: The theory of nonlocal elasticity is developed. Balance laws, jump conditions and the second law of thermodynamics are given. By means of axioms of nonlocality, objectivity and the entropy inequality, the constitutive equations are derived for nonlocal elastic solids. The field equations are obtained and applied to study the propagation of body and surface waves.

Beam Buckling by Finite Element Procedure

Abstract: A finite element procedure for determining the critical buckling load for three-dimensional structures idealized by planar two-dimensional elements is presented. This procedure is applicable to structures whose instabilities involve small displacements and elastic behavior, i.e., linear elastic buckling. Local and overall structural instabilities may be treated together with complex loading and support conditions. The smallest eigenvalue corresponding to the smallest buckling load is determined by an inverse iteration procedure. The accuracy of this finite element procedure is evaluated by comparison with a number of problems for which classical solutions are available. A simply supported wide-flange beam with a stiffener, lateral restraints, and various rotational restraints is presented to illustrate the versatility of the procedure as well as the effect of the restraints on the buckling load. In addition, a comparison between the subject procedure and recent experimental results on a continuous wide-flange beam is presented.

The Linear Theory of Micropolar Elasticity

Abstract: The classical theory of elasticity describes well the behaviour of construction materials (various sorts of steel, aluminium, concrete) provided the stresses do not exceed the elastic limit and no stress concentration occurs.

Theory of Elasticity

Abstract: This book is designed for use by students and teachers in the field of applied mechanics and mathematics, and for practitioners in civil and mechanical engineering Since tensor calculus is an indispensable prerequisite when dealing with the theory of elasticity in a modern way, the first part of the book consists in an introduction into this subject In the second part, the physical foundations of the theory of elasticity are given, including nonlinearities The excursion into the field of geometric and physical nonlinearities is done in order to prepare the reader for further advances into the most recent developments of the theory The book itself, in the remainder, is restricted to linear problems only The third part of the book deals with the mathematical theory of linear elasticity in full extent Curvilinear problems, two- and three-dimensional problems are included Stress has been put on working out a systematic approach to the solutions of all kinds of stress states, not neglecting triaxial problems Also, energy methods have been dealt with, taking into account the generalization and extension of these methods by Rudiger and Reiss ner The fourth and last part of the book consists in an application of the general methods, as outlined in part 3, to special structures like plates and shells, thus giving hopefully something of interest to the practising engineer"

Elastic Analysis of Frameworks with Elastic Connections

Abstract: Rectilinear plane and space frame with elastic connections occur in building frames; and with diagonal bracings, they also occur in scaffolding. The matrix stiffness analysis of the general space frame is developed for linear elastic connections related to every possible displacement at the end of each member. Correction matrices are also derived for modifying the usual rigid joint analysis. Examples are given of the elastic analysis of a plane framework and a simple space portal allowing for various elastic connections at the ends of some or all of the members.

Elastic Analysis of Zoned Orthotropic Continua

Abstract: A method is presented for determining the stresses and displacements, under plane strain or plane stress conditions, in a linear elastic multizoned continuum having an irregular boundary geometry. Each zone is homogeneous and consists in general of a different orthotropic material, with one plane of elastic symmetry parallel to the problem plane, and the other two planes orientated arbitrarily. The singular solution used is that for a point load acting within a homogeneous orthotropic infinite lamina. The derivation of this new solution is given. Since the principle of superposition applies, the numerical integration of multiples of such singular solutions around zone boundaries produces a result satisfying both the governing equations and the zone boundary conditions on discrete boundary elements. The main advantage of the method is that, since only the boundary is discretized, the system of equations is small compared with other numerical methods.

Some Mechanical Properties of Sintered Fiber Metal Composites

Abstract: Kinked, short-length, fine wire can be molded by conventional powder metallurgy procedures and sintered to a porous composite with large proportions of interconnecting voids. This material has potential applications for implanted prosthetic systems. The material behaves in a nonlinear elastic fashion which may be approximated as two linear elastic processes. In the strain range of 0 to about 0.5 percent, the elastic modulus can be less than 1 kg/mm2. In a higher strain regime the elastic modulus is about 100 kg/mm2. A total elastic strain range of 1.5 to 4 percent is found.

Inelastic Analysis of Reinforced Concrete Frames

Abstract: The imposed rotation method for the inelastic analysis of frames rests on the interpretation of the actual bending moment distribution as the superposition of linear elastic moment responses to loads and to unknown plastic rotations regarded as imposed strains. The method given herein is a generalized formulation, covering second-order geometric effects and moment-axial force interaction. Finite element models of frames and piecewise linear moment-rotation laws for critical sections are assumed. Recent algorithms for solving quadratic programming and linear complementarity problems are shown to be efficiently applicable to the analysis of multistory frames. The safety factor with respect to local failure because of “brittle” flexural behavior turns out to be attainable by a suitably modified linear programming procedure.

Mechanics of a Deformed Solid

Abstract: : The book gives a cursory survey of the major trends in the mechanics of solids in the USSR over the past 50 years. The major topics discussed are: Linear elasticity theory, nonlinear elasticity theory, plasticity theory, creep theory, the creep of aging materials, the mechanics of soils, the theory of elastic shells and plates, the dynamics of deformable solids, the stability of elastic and non-elastic systems and the mechanics of fracture.

Nonlinear Bending of Elastic Plates of Variable Profile

Abstract: The technique of dynamic relaxation is invoked in analyzing the nonlinear bending of circular plates of linear elastic material and variable profile subjected to a uniformly distributed lateral loading. Results for clamped plate with exponential profile and for pinned edged plates with linear profile are presented. Comparison of these results for a uniform plate with the available results shows excellent correlation ascertaining the efficiency of the technique. The results from extensive numerical experiments are presented in such a form as to reflect the effect of variable profile, in particular, on the boundary layer phenomenon. Approximate estimates for the values of the important parameters, i.e., the time increment and damping coefficients, are suggested.

Hypoelastic form of equations in nonlinear elasticity theory

Abstract: It is shown that the complete system of equations of elasticity theory for an isotropic medium admits a unique representation in the hypoelastic form (the tensor of the rate of change of stresses is a linear function of the tensor of strain rates with coefficients depending on the invariants of the stress tensor). It is necessary to this end that the hypothesis be satisfied on the determination of strains by stresses which are unknown. Any arbitrariness in the choice of the coefficients of the hypoelastic relation may result in the thermodynamic identity being infringed.

Integration of differential equations in elastostatics through-determination of the mean stress

Abstract: The paper is devoted to discussion and development of an analytical method, proposed by the author, for integration of differential equations in elastostatics. A homogeneous isotropic linear elastic body is considered. The differential equations are first formulated in terms of the displacement components (u, v, w) and the mean normal stress (p) for any real value of Poisson's ratio in the interval — 1 < v ≤ 1/2. By this means we obtain in a three-dimensional case a set of four equations in four unknown functions, and in a plane (two-dimensional) case – a set of three equations in three, both sets (unlike Navier's equations) being valid for incompressible bodies (v = 1/2) as well. Derivation of their solution is based on the condition of single-valuedness of the mean normal stress at any point of the body, with displacements presented by means of the Stokes-Helmholtz resolution of vector fields. Integration of this type of differential equations was first studied by the author in works on the deformation of nonhomogeneous elastic incompressible bodies, and carried further in works on elastostatic problems of incompressible and compressible bodies, both homogeneous and nonhomogeneous.

Influence of Anisotropy and Soil Structure on Elastic Properties of Sediments

Abstract: The theory of elasticity is used for the solution of sediment sound propagation as well as various stress distribution and soil deformation problems. This requires the determination of sediment elastic constants; yet there are many factors that make the rational and accurate prediction of field stress-strain relationship from the results of laboratory tests difficult. One of these important factors is that the soil is not an isotropic linear elastic material having a unique Young’s modulus, E.

Dynamic Response and Fatigue Characteristics of Asphaltic Mixtures

Abstract: This investigation deals with the influence of several mix variables in respect to asphaltic concrete on its fatigue response. The investigation was based on a simple model representation comprising a beam supported on elastic foundation subjected to sinusoidal repeated loading, thus providing a two-dimensional simulation of actual pavement conditions under traffic loads. The dimensions of the beam were designed such that plan strain conditions prevailed during fatigue loading. Fracture mechanics concepts using linear elastic theory were employed to analyze test data, including stress and deformation near the crack tip. It was also hypothesized that the parameter, A, in the rate-of-crack-growth equation, dc/dN = A K 4 would adequately reflect the changes induced in the fatigue response of the mix by the selected mix variables. The effect of mixture variables such as the amount of binder, density, aging, and viscosity on the parameter A is investigated.

Internal Stresses in Crystals and in the Earth

Abstract: It is shown that the two important permanent deformation modes, namely plastic and viscous deformation, occur in similar form in crystals and in the earth. Earth quakes are compared with recovery phenomena in crystals and parallels are drawn between the sciences of the seismology in the earth and the acoustic emission in crystals. In a quantitative part the method of the modified Green functions is described which allows us to write complex results in a very condensed form. Hereby we confine ourselves to linear elasticity theory. The method also allows us to determine external and internal stresses in favourable situations.

Response of Polymers to Tensile Impact. 2. Extension of the Integral-Equation, Successive-Substitution Solution to Non-Linear, Time-Independent Materials

Abstract: : An integral-equation, successive- substitution solution for the propagation of strain waves in a linear elastic material, developed in an earlier paper, is here extended to non-linear materials without creep (time-independent materials) A PREVIOUSLY-PUBLISHED PROBLEM, BASED ON EXPERIMENTAL DATA FOR NYLON STRING IS SOLVED BY THE SUCCESSIVE-SUBSTITUTION METHOD AND COMPARED WITH THE EARLIER SOLUTION OBTAINED BY THE METHOD OF CHARACTERISTICS The agreement of the two solutions is at first good, but in the region where the stress-strain curve of the nylon is concave upward a tendency to oscillation builds up and the solution eventually oscillates This occurs in approximately the same region where shock waves can appear in a method-of-characteristics solution Oscillations in the strained portion of a string are examined theoretically and it is shown that the energy of standing waves can be used to obtain energy conservation Although the successive-substitution method generates oscillations when it has to deal with a discontinuity in strain, the possibility that oscillations also actually exist as a means of conserving energy cannot be ruled out

An axisymmetric finite element analysis of the mechanical and thermal stresses in brake drums

Abstract: A linear elastic finite element analysis of brake drums is presented. The axisymmetry is assumed for the geometry of the structure; however the loads may be arbitrary. Laboratory measurements of the mechanical stresses support the computational analysis.