Showing papers in "Journal of Applied Mechanics in 1975"
TL;DR: The finite element method (FEM) is a numerical technique used to perform finite element analysis of any given physical phenomenon as discussed by the authors, such as structural or fluid behavior, thermal transport, wave propagation, and the growth of biological cells.
Abstract: Introduction to finite element analysis: 1.1 What is ... The finite element method (FEM) is a numerical technique used to perform finite element analysis of any given physical phenomenon. It is necessary to use mathematics to comprehensively understand and quantify any physical phenomena, such as structural or fluid behavior, thermal transport, wave propagation, and the growth of biological cells.
1,811 citations
TL;DR: In this paper, the Kelvin-Voigt model is shown to be logically untenable, for it indicates that the bodies must exert tension on one another just before separating, and it denotes that the damping energy loss is proportional to the square of the impacting velocity, instead of to its cube.
Abstract: During impact the relative motion of two bodies is often taken to be simply represented as half of a damped sine wave, according to the Kelvin-Voigt model. This is shown to be logically untenable, for it indicates that the bodies must exert tension on one another just before separating. Furthermore, it denotes that the damping energy loss is proportional to the square of the impacting velocity, instead of to its cube, as can be deduced from Goldsmith's work. A damping term $\lambda x^n \dot{x} $ is here introduced; for a sphere impacting a plate Hertz gives $n = 3/2$. The Kelvin-Voigt model is shown to be approximated as a special case deducible from this law, and applicable when impacts are absent. Physical experiments have confirmed this postulate.
1,390 citations
TL;DR: In this paper, a set of constitutive equations has been formulated to represent elastic-viscoplastic strain hardening material behavior for large deformations and arbitrary loading histories, and the total deformation rate is considered to be separable into elastic and inelastic components which are functions of state variables at all stages of loading and unloading.
Abstract: : A set of constitutive equations has been formulated to represent elastic-viscoplastic strain hardening material behavior for large deformations and arbitrary loading histories. An essential feature of the formulation is that the total deformation rate is considered to be separable into elastic and inelastic components which are functions of state variables at all stages of loading and unloading. The theory, therefore, is independent of a yield criterion or loading and unloading conditions. The deformation rate components are determinable from the current state which permits an incremental formulation of problems. Strain hardening is considered in the equations by introducing plastic work as the representative state variable. The problem of uniaxial straining has been examined for a number of histories that included straining at various rates, rapid changes of strain rate, unloading and reloading, and stress relaxation. The calculations were based on material constants chosen to represent commercially pure titanium. The results are in good agreement with corresponding experiments on titanium specimens. (Author)
942 citations
TL;DR: In this article, it was shown that the combination resonances appear to involve the differences, rather than the sums, of the low frequencies involved in a cantilevered pipe conveying fluid.
Abstract: We are very grateful to Professor Iwatsubo for his discussion of our paper. Concerning his first point, there appears to be some contradiction between the second and third paragraphs of the Discussion. However, we agree with the first statement made by the discusser that, for cantilevered columns, both sum and difference-type combination resonances are possible. In our paper, concerning cantilevered pipes conveying fluid, we were careful to say that \"the combination resonances appear to involve the differences, rather than the sums.\" We have not made a special study of this, and our supposition was based on the consideration that for the low frequencies involved it is more likely that the combination resonances be of the difference rather than the sum type, since in the latter case (co; + a>y)/fc near zero would imply very large values of k. Concerning the second point, the limited extent of our calculations does not allow us to say with certainty that, let us say, first-mode parametric resonances are impossible for all possible sets of system parameters. However, we have never found such instabilities in our analysis, nor has it ever been found in the experiments [1] . A possible explanation is this. In the cantilevered pipe the Coriolis acceleration acts effectively as a damping force and the effective damping varies from one mode to another [2]. It is certainly possible that some modes are simply too heavily \"damped\" by the Coriolis effect to exhibit parametric resonances, either over a wide range of flow velocities or for all flow velocities.
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TL;DR: In this paper, the authors present an analysis of the behavior of composite materials and their properties, such as bending, buckling, and vibration of Laminated Plates, as well as the maximum and minima of functions of a single variable.
Abstract: 1.Introduction to Composite Materials 2. Macrochemical Behavior of a Lamina 3.Micromechanical Behavior of a Lamina 4.Macromechanical Behavior of a Laminate 5.Bending, Buckling, and Vibration of Laminated Plates 6.Other Analysis and Behavior Topics 7.Introduction to Design of Composite Structures Appendix A.Matrices and Tensors Appendix B.Maxima and Minima of Functions of a Single Variable Appendix C.Typical Stress-Strain Curves Appendix D.Governing Equations for Beam Equilibrium and Plate Equilibrium, Buckling, and Vibration Index
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TL;DR: In this paper, the central impact of a mass on a simply-supported laminated composite plate under initial stress is investigated, and the contact force and the dynamic response of the plate are obtained by solving a non-linear integral equation.
Abstract: : The central impact of a mass on a simply-supported laminated composite plate under initial stress is investigated. The contact force and the dynamic response of the plate are obtained by solving a non-linear integral equation. The energy transferred from the mass to the plate during impact is also obtained by use of a normalized contact force. It is found that a higher initial tensile stress elevates the maximum contact force, but reduces the contact time, the deflection, and the stresses. It is also noted that a higher tensile initial stress results in less energy transfer from the striking mass to the plate.
TL;DR: In this article, an exact elastic-plastic solution for the stresses in an infinite sheet having a circular hole subject to pressure is obtained on the basis of J2 deformation theory together with a modified Ramberg-Osgood law.
Abstract: An exact elastic-plastic solution for the stresses in an infinite sheet having a circular hole subject to pressure is obtained on the basis of J2 deformation theory together with a modified Ramberg-Osgood law. The sheet is orthotropic but isotropic in its plane. The results are assessed on the basis of Budiansky's criterion for the acceptability of J2 deformation theory. By using exact elastic-plastic stresses, the function connecting the pressure at the hole with the radial enlargement is obtained. Upon release of the pressure, residual stresses around the hole are produced.
TL;DR: In this paper, an infinite elastic solid containing a double-periodic rectangular array of slit-like cracks is considered, and the cracks are represented as suitable distributions of dislocations which are determined from a singular integral equation.
Abstract: An infinite elastic solid containing a double-periodic rectangular array of slit-like cracks is considered. The solid is subjected to a uniform stress resulting in a state of plane strain. The cracks are represented as suitable distributions of dislocations which are determined from a singular integral equation. This equation is solved numerically in an efficient manner using an expansion of the non-singular part of the kernel in a series of Chebyshev polynomials. Values of the stress intensity factors are presented, as well as the change in strain energy due to the presence of the cracks. Also, the effective elastic constants of a sheet having a rectangular array of cracks are given as functions of the crack spacing.
TL;DR: In this paper, a method for solving three-dimensional mixed-boundary-value problems arising in elastostatics is discussed. But the method is applied to a plate of finite thickness which contains a finite, through the thickness, line crack.
Abstract: This paper discusses a method for solving three-dimensional mixed-boundary-value problems which arise in elastostatics. Specifically, the method is applied to a plate of finite thickness which contains a finite, through the thickness, line crack. The analysis shows that (a) in the interior of the plate only the stresses sigma-x, sigma-y, sigma-z, and tau-xy are singular of order 1/2; (b) in the vicinity of the corner point all the stresses are singular of order ((1/2) plus 2 nu); as the thickness h approaches infinity the plane strain solution is recovered and; (d) as nu approaches o the plane stress solution is recovered. Finally, it is found that in the neighborhood of the corner points, even though the displacements are singular for certain values of the Poisson's ratios, the derived stress field satisfies the condition of local finite energy. /Author/
TL;DR: In this article, the near-tip angular variations of elastodynamic stress and displacement fields are investigated for rapid transient crack propagation in isotropic and orthotropic materials, and it is shown that p = 0.5.
Abstract: The near-tip angular variations of elastodynamic stress and displacement fields are investigated for rapid transient crack propagation in isotropic and orthotropic materials. The 2-dimensional near-tip displacement fields are assumed in the general form r/sup P/ T(t, c) K(theta, c), where c is a time-varying velocity of crack propagation, and it is shown that p = 0.5. For isotropic materials, K(theta, c) is determined explicitly by analytical considerations. A numerical procedure is employed to determine K(theta, c) for orthotropic materials. The tendency of the maximum stresses to move out of the plane of crack propagation as the speed of crack propagation increases is more pronounced for orthotropic materials, for the case that the crack propagates in the direction of the larger elastic modulus. The angular variations of the near-tip fields are the same for steady-state and transient crack propagation, and for propagation along straight and curved paths, provided that the direction of crack propagation and the speed of the crack tip vary continuously.
TL;DR: In this article, a mathematical model is developed and methods of analysis are formulated for determining the structural response of textile fabric flat panels subjected to ballistic impact by a dense projectile, which is suitable for either desk calculator use or for a digital computer in calculating strains, projectile position, forces, and decelerations as functions of time.
Abstract: A mathematical model is developed and methods of analysis are formulated for determining the structural response of textile fabric flat panels subjected to ballistic impact by a dense projectile. A stepwise procedure in time is formulated which is suitable for either desk calculator use or for a digital computer in calculating strains, projectile position, forces, and decelerations as functions of time. Analytical results are compared with experimental data for impact of a .22 caliber fragment simulator impacting 1 ply and 12 ply nylon cloth as well as Kevlar (PRD)-49-IV cloth from 1–24 plies.
TL;DR: In this article, the linear theory of Shells is used to describe the three-dimensional elasticity of a surface and the effect of virtual work and boundary conditions on the potential energy of a shell.
Abstract: I The Linear Theory of Shells.- 1 Geometry of Surfaces.- 1.1 Geometric Relations for Surfaces.- 1.2 Lines of Curvature.- 1.3 Surfaces of Revolution.- 1.4 Parallel Surfaces.- 1.5 Small Deformations of a Surface.- 2 The Linear Theory of Transversely Rigid Shells.- 2.1 Fundamental Definitions.- 2.2 Equations of Three-Dimensional Elasticity.- 2.3 Assumptions of Shell Theory.- 2.4 Displacements and Strains.- 2.5 Stress Resultants and Equilibrium Equations.- 2.6 Statically Equivalent Force Systems.- 2.7 Overall Force-Strain Relations.- 2.8 The Principle of Virtual Work and Boundary Conditions.- 2.9 Strain Energy and the Principle of Minimum Potential Energy.- 2.10 Stress Functions.- 2.11 Transverse Shear and Normal Stresses.- Appendix Boundary Conditions at Edges which are Not Lines of Curvature.- 3 Simplifications of Shell Theory.- 3.1 Modification of Overall Force-Strain Relationships.- 3.2 Internal Stress Distribution.- 3.3 Approximate Reduction of Shell Theory: Vlasov's Equations.- 3.4 Shallow Shells.- 3.5 Exact Reduction of Shell Theory for Zero Poisson's Ratio (I) Complex Stress Resultants.- 3.6 Exact Reduction of Shell Theory for Zero Poisson's Ratio (II) Complex Displacements.- 3.7 Approximate Reduction of Shell Theory for Nonzero Poisson's Ratio.- 3.8 The Membrane Theory of Shells.- 3.9 Transformation of the Equations of Membrane Theory.- II Axisymmetric Deformations of Shells of Revolution.- 4 The Cylindrical Shell.- 4.1 General Relations for Cylindrical Shells.- 4.2 Edge-Loaded Cylindrical Shells.- (A) Semi-Infinite Cylinder.- (B) Symmetrically Loaded Finite Cylinder.- (C) Antisymmetrically Loaded Finite Cylinder.- (D) Finite Cylinder Loaded at One Edge.- 4.3 Particular Integrals for Surface-Loaded Cylindrical Shells.- 4.4 Some Solutions of Cylindrical Shell Problems.- (A) Compressed Cylinder with Rigid End Rings.- (B) Pressurized Cylinder with Rigid Movable End Plates.- (C) Effect of Restraint of Longitudinal Movement.- (D) Effect of End Plate Flexibility.- 4.5 Pressurized Cylinder with an Abrupt Thickness Change.- 4.6 Cylinder in a Rigid Collar.- 5 The Conical Shell.- 5.1 General Relations for Conical Shells.- 5.2 Solution of the Homogeneous Deflection Equation.- 5.3 Edge-Loaded Conical Shells.- (A) Semi-Infinite Cones.- (B) Complete Cones.- (C) Finite Conical Frustums.- 5.4 Particular Solutions of the Conical Shell Equations.- 5.5 Complete Conical Shell Subjected to External Pressure.- 6 The Spherical Shell.- 6.1 General Relations for Spherical Shells.- 6.2 A Particular Solution of the Bending Equations.- 6.3 Some Relations for the Complementary Solution.- 6.4 Solutions by Means of Legendre Functions.- 6.5 Shallow Spherical Shells.- 6.6 Closed Spherical Cap under Edge Loading.- 6.7 Tangent Cone Approximation.- 6.8 Particular Solutions for Spherical Shells.- 6.9 Complete Sphere Subjected to Internal or External Pressure.- 6.10 Spherical Shell with Concentrated Loads at the Poles.- 6.11 Spherical Cap Loaded at the Apex.- 6.12 Effect of Method of Load Application.- 7 Shells of Arbitrary Meridian.- 7.1 General Equations for Arbitrary Shells of Revolution.- 7.2 An Approximate Complementary Solution of the Bending Equations.- 7.3 The Variable ?.- 7.4 Approximate Complementary Solutions Valid at Points with Horizontal Tangents.- 7.4.1 The Ellipsoidal Shell.- 7.4.2 The Circular Toroidal Shell.- 7.5 Membrane Theory as a Particular Solution of the Bending Equations.- 7.6 Some Particular Solutions for Circular Toroidal Shells.- 8 Torsion and Circumferential Bending of Shells of Revolution.- 8.1 Torsion of Shells of Revolution.- 8.2 Circumferential Bending of Shells of Revolution.- III Asymmetrically Loaded Shells.- 9 Asymmetric Deformations of Spherical Shells.- 9.1 General Relations for Asymmetrically Loaded Spherical Shells.- 9.2 'Wind' Loading of Spherical Shells.- 9.3 Edge-Loaded Spherical Shells: Inextensional Deformations and Membrane Stress States.- 9.4 Complex Variable Representation of Membrane Stress States.- 9.5 Edge-Loaded Spherical Shells: Mixed Bending-Stretching Solutions.- 9.6 Bending of a Spherical Shell by Moments at the Poles: Exact Solution.- 9.7 Bending of a Spherical Shell by Moments at the Poles: Shallow Shell Theory.- 9.8 Bending of a Spherical Shell by Tangential Loads.- 9.9 Some Other Problems of Edge-Loaded Spherical Shells.- 9.10 Surface-Loaded Spherical Shells.- 10 Asymmetric Deformations of Circular Cylindrical Shells.- 10.1 General Relations for Cylindrical Shells.- 10.2 Simplifications of the Equations for Radial and Edge Loading.- 10.3 Cylinders Loaded Along Circular Edges.- 10.4 End-Loaded Cantilevered Cylinder with a Rigid End Ring.- 10.5 Infinite Cylindrical Shell Loaded By Diametrically Opposed Concentrated Loads.- 10.6 Results for Some Other Concentrated Loads.- 10.7 Particular Solutions for Complete Cylindrical Shells.- 10.8 Edge-Loaded Cylindrical Strips.- 10.9 Infinite Cylindrical Strips.- 10.10 Stress Concentration Around Holes.- 10.10.1 Effect of a Hole on a Circular Cylinder under Uniform Tension.- 11 Results for Other Shells.- 11.1 'Wind' Loading of Arbitrary Shells of Revolution.- 11.2 Conical Frustums Subjected to End Loads.- 11.3 Numerical Solution of the Bending Equations for Shells Of Revolution.- 11.4 Shallow Translational Shells.- 11.5 Finite Element Analysis of Shells of Arbitrary Middle Surface.- 12 Nonuniform Anisotropic Shells.- 12.1 Necessity for Modifications of the Theory of Shells.- 12.2 Effect of Thermal Loading.- 12.3 Effect of Nonuniform Wall Thickness.- 12.3.1 Derivation of Equations for Shells of Nonuniform Wall Thickness.- 12.3.2 Axisymmetric Deformations of Nonuniformly Thick Shells of Revolution.- 12.3.3 Cylindrical Shell of Linearly Varying Thickness.- 12.3.4 Conical Shell of Linearly Varying Thickness.- 12.4 Effects of Anisotropy.- 12.5 Layered Shells.- 12.6 Stiffened Shells.- IV Dynamics of Shells.- 13 Free Vibrations of Shells.- 13.1 Equations of Motion.- 13.2 Free Harmonic Vibrations.- 13.3 Orthogonality Conditions for Vibration Mode Shapes.- 13.4 Free Vibrations of Cylindrical Shells.- 13.4.1 Simply Supported Cylindrical Shells.- 13.4.2 Minimum Frequency of Vibration.- 13.4.3 Effects of Other Edge Conditions.- 13.5 Free Vibrations of Spherical Shells.- 13.5.1 Vibrations of Spherical Shell Segments.- 13.5.2 Torsional Vibrations of Spherical Caps.- 13.5.3 Approximate Solutions for Shallow Spherical Caps.- 13.5.4 Vibrations of Complete Spherical Shells.- 13.6 Vibration Characteristics of Conical Shells.- 14 Response of Shells to Dynamic Loading.- 14.1 Solution of Initial Value Problems.- 14.2 Solution of Problems Involving Time-Dependent Surface or Edge Loading.- 14.3 Periodic Surface and Edge Forces.- 14.4 Solution of Problems Involving Time-Dependent Edge Displacements.- 14.5 Some Examples of Modal Analysis.- 14.6 Other Methods of Solution of Shell Response Problems.- Author Index.
TL;DR: The Symposium of the International Union of Theoretical and Applied Mechanics (IUTAM), Enschede, Netherlands, 20-23 Agust 1974 as discussed by the authors was the first edition of the Symposium.
Abstract: Proceedings of the Symposium of the International Union of Theoretical and Applied Mechanics (IUTAM), Enschede, Netherlands, 20-23 Agust 1974.