scholarly journals Closed-Form Solutions for a Mode-III Moving Interface Crack at the Interface of Two Bonded Dissimilar Orthotropic Elastic Layers

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
B. M. Singh ◽  
J. Rokne ◽  
R. S. Dhaliwal
Keyword(s):  
Closed Form ◽  
Integral Transform ◽  
Practical Importance ◽  
Leading Edge ◽  
Shear Stresses ◽  
Mode Iii ◽  
Closed Form Solutions ◽  
Moving Interface ◽  
Elastic Layers ◽  
Physical Quantities

An integral transform technique is used to solve the elastodynamic problem of a crack of fixed length propagating at a constant speed at the interface of two bonded dissimilar orthotropic layers of equal thickness. Two cases of practical importance are investigated. Firstly, the lateral boundaries of the layers are clamped and displaced in equal and opposite directions to produce antiplane shear resulting in a tearing motion along the leading edge of the crack, and secondly, the lateral boundaries of the layers are subjected to shear stresses. The analytic solution for a semi-infinite crack at the interface of two bonded dissimilar orthotropic layers has been derived. Closed-form expressions are obtained for stressing the intensity factor and other physical quantities in all cases.

scholarly journals Revisiting the rocking block: closed-form solutions and similarity laws

2012 ◽  
Vol 468 (2144) ◽  
pp. 2294-2318 ◽  
Author(s):  
Elias G. Dimitrakopoulos ◽  
Matthew J. DeJong
Keyword(s):  
Closed Form ◽  
Base Excitation ◽  
Closed Form Solutions ◽  
Rocking Block ◽  
Pulse Type ◽  
Self Similar ◽  
Physical Quantities ◽  
Similarity Laws ◽  
Shed Light ◽  
Rocking Response

In this paper, the dynamic response of the rocking block subjected to base excitation is revisited. The goal is to offer new closed-form solutions and original similarity laws that shed light on the fundamental aspects of the rocking block. The focus is on the transient dynamics of the rocking block under finite-duration excitations. An alternative way to describe the response of the rocking block, informative of the behaviour of rocking structures under excitations of different intensity, is offered. In the process, limitations of standard dimensional analysis, related to the orientations of the involved physical quantities, are revealed. The proposed dimensionless and orientationless groups condense the response and offer a lucid depiction of the rocking phenomenon. When expressed in the appropriate dimensionless–orientationless groups, the rocking response becomes perfectly self-similar for slender blocks (within the small rotations range) and practically self-similar for non-slender blocks (larger rotations). Using this formulation, the nonlinear and non-smooth rocking response to pulse-type ground motion can be directly determined, and need only be scaled by the intensity and frequency of the excitation.

Elasticity Approach to Load Transfer in Cord-Composite Materials

2009 ◽  
Vol 76 (6) ◽  
Author(s):  
Anthony J. Paris
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Axial Force ◽  
Load Transfer ◽  
Axial Loading ◽  
Shear Stresses ◽  
Matrix Interface ◽  
Closed Form Solutions ◽  
Apparent Modulus ◽  
Reinforced Composite

An elasticity approach to the mechanics of load transfer in cord-reinforced composite materials is developed. Finite cords embedded in an elastic matrix and subjected to axial loading is considered, and the extension-twist coupling of the cords is taken into account. Closed form solutions for the axial force and twisting moment in the cord, the shear stresses at the cord-matrix interface in the axial and circumferential directions, the effective axial modulus of the cord, and the apparent modulus of the cord composite are presented. An example of a cord composite typical of what can be found in steel-belted-radial tires is used to illustrate the results. It was found that large shear stresses occur at the cord-matrix interface in both the axial and circumferential directions at the cord ends and that the effective modulus of the cords may be greatly reduced. As a result, the apparent modulus of the composite may be significantly less than that found by a conventional application of the rule-of-mixtures approach.

scholarly journals Two-Dimensional Electrostatic Problem in a Plane with Earthed Elliptic Cavity due to One or Two Collinear Charged Electrostatic Strips

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
B. M. Singh ◽  
J. G. Rokne ◽  
R. S. Dhaliwal
Keyword(s):  
Charge Density ◽  
Closed Form ◽  
Integral Equations ◽  
Integral Transform ◽  
Weight Functions ◽  
Two Dimensional ◽  
Electrostatic Problem ◽  
Closed Form Solutions ◽  
Triple Integral Equations ◽  
Elliptic Cavity

A two-dimensional electrostatic problem in a plane with earthed elliptic cavity due to one or two charged electrostatic strips is considered. Using the integral transform technique, each problem is reduced to the solution of triple integral equations with sine kernels and weight functions. Closed-form solutions of the set of triple integral equations are obtained. Also closed-form expressions are obtained for charge density of the strips. Finally, the numerical results for the charge density are given in the form of tables.

Fully Developed Sliding of Rough Surfaces

1989 ◽  
Vol 111 (3) ◽  
pp. 445-451 ◽  
Author(s):  
C. Liu ◽  
B. Paul
Keyword(s):  
Closed Form ◽  
Contact Region ◽  
Tangential Force ◽  
Normal Pressure ◽  
Shear Stresses ◽  
Closed Form Solutions ◽  
Pressure Distributions ◽  
The Coefficient Of Friction ◽  
Force Components ◽  
Instantaneous Center

Given the contact region between two bodies, the normal pressure distribution over the contact region, and the coefficient of friction, we seek to find all combinations of tangential forces and twisting moment (about the normal to the contact surface) for which fully developed sliding impends. As part of the solution we must determine the distribution of the surface tractions (shear stresses) and the location of the instantaneous center (IC) of the impending motion. New closed form solutions of the stated problem are found for circular contact patches with pressure distributions corresponding to (a): a flat stamp; and (b): elastic spheroids with Hertzian pressure distributions. For contact regions other than circular, no closed form solutions are known. We have developed numerical procedures to solve for arbitrary contact patches, with arbitrary distributions of normal pressure, and present carpet plots of tangential force components (Fx, Fy) and IC coordinates for the following cases: flat ellipsoidal stamps; ellipsoidal indenters (Hertzian pressure); and a non-Hertzian, nonelliptical contact of a rail and wheel. Level curves of twisting moment Mz versus tangential force components are provided. Given any two of the three quantities (Fx, Fy, Mz), the algorithms and the plots in this paper make it possible and convenient to find the remaining force or moment which will cause gross sliding to impend, for virtually arbitrary contact regions and arbitrary pressure distributions.

scholarly journals Closed-form solutions of hole distortion for use in deep-hole drilling measurements of residual stress in orthotropic plates

2016 ◽  
Vol 52 (2) ◽  
pp. 77-82 ◽  
Author(s):  
Carlos Garza ◽  
Anton Shterenlikht ◽  
Martyn J Pavier ◽  
David J Smith
Keyword(s):  
Residual Stress ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Hole Drilling ◽  
Shear Stresses ◽  
Deep Hole ◽  
Element Analysis ◽  
Deep Hole Drilling ◽  
Closed Form Solutions

The measurement of residual stress using the deep-hole drilling method relies on the evaluation of the distortion of a hole in a plate under the action of far-field direct and shear stresses. While closed-form solutions exist for the isotropic materials, in previous work for orthotropic materials, finite element analysis has been used to find the distortion. In this technical note, Lekhnitskii’s analysis is used to find closed-form solutions for the distortion of a circular hole in an orthotropic plate. The results are compared with those of finite element analysis for a range of material properties with excellent agreement.

scholarly journals Stationary Dynamic Displacement Solutions for a Rectangular Load Applied within a 3D Viscoelastic Isotropic Full Space—Part I: Formulation

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Euclides Mesquita ◽  
Edivaldo Romanini ◽  
Josue Labaki
Keyword(s):  
Closed Form ◽  
Integral Transform ◽  
Physical Space ◽  
Integral Transforms ◽  
Fourier Integral ◽  
Constant Load ◽  
Wave Number ◽  
Dynamic Displacement ◽  
Closed Form Solutions ◽  
Fourier Integral Transform

A dynamic stationary semianalytical solution for a spatially constant load applied over a rectangular surface within a viscoelastic isotropic full space is presented. The solution is obtained within the frame of a double Fourier integral transform. Closed-form solutions for general loadings within the full space are furnished in the transformed wave number domain. Expressions for three boundary value problems, associated to a normal and two tangential rectangular loadings in the original physical space, are given in terms of a double inverse Fourier integral. These inverse integral transforms must be evaluated numerically. In the second part of the present paper a strategy to evaluate these integrals is described, the procedure validated and a number of original results are reported.

Sign in / Sign up

Export Citation Format

Share Document