Transient Response of an Infinite Elastic Medium Containing a Spherical Cavity Subjected to Torsion

1999 ◽  
Vol 67 (2) ◽  
pp. 282-287 ◽  
Author(s):  
U. Zakout ◽  
Z. Akkas ◽  
G. E. Tupholme
Keyword(s):  
Elastic Medium ◽  
Transient Response ◽  
Spherical Cavity ◽  
Laplace Transformation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Shear Stresses ◽  
Surface Loading ◽  
Transformation Techniques ◽  
Isotropic Elastic Medium

An exact closed-form solution is obtained for the transient response of an infinite isotropic elastic medium containing a spherical cavity subjected to torsional surface loading using the residual variable method. The main advantage of the present approach is that it eliminates the computational problems arising in the existing methods which are primarily based on Fourier or Laplace transformation techniques. Extensive numerical results for the circumferential displacements and shear stresses at various locations are presented graphically for Heaviside loadings. [S0021-8936(00)01102-8]

A closed-form solution for composite tunnel linings in a homogeneous infinite isotropic elastic medium

2008 ◽  
Vol 45 (2) ◽  
pp. 266-287 ◽  
Author(s):  
Hany El Naggar ◽  
Sean D. Hinchberger ◽  
K. Y. Lo
Keyword(s):  
Closed Form ◽  
Elastic Medium ◽  
Closed Form Solution ◽  
Form Solution ◽  
Tunnel Lining ◽  
Linear Elastic ◽  
Isotropic Elastic Medium ◽  
Thin Walled ◽  
Walled Cylinder ◽  
Elastic Soil

This paper presents a closed-form solution for composite tunnel linings in a homogeneous infinite isotropic elastic medium. The tunnel lining is treated as an inner thin-walled shell and an outer thick-walled cylinder embedded in linear elastic soil or rock. Solutions for moment and thrust have been derived for cases involving slip and no slip at the lining–ground interface and lining–lining interface. A case involving a composite tunnel lining is studied to illustrate the usefulness of the solution.

Transient Response of an Elastic Homogeneous Half-Space to Suddenly Applied Rectangular Loading

1994 ◽  
Vol 61 (2) ◽  
pp. 256-263 ◽  
Author(s):  
F. Guan ◽  
M. Novak
Keyword(s):  
Laplace Transform ◽  
Half Space ◽  
Transient Response ◽  
Integral Kernel ◽  
Closed Form Solution ◽  
Contact Problems ◽  
Form Solution ◽  
Inverse Laplace Transform ◽  
Line Load ◽  
Homogeneous Half Space

A closed-form solution of transient response to suddenly applied loading distributed over a rectangular area on the surface of an elastic homogeneous half-space is developed for special purposes such as analysis of dynamic soil-structure interaction or contact problems. The solution is obtained using Laplace transform with respect to time and Fourier transform with respect to space. Inverse Laplace transform is implemented analytically. As extreme cases of rectangular loading, the solutions for a point force or finite line load can also be obtained. The advantages of this solution over most other solutions by numerical analyses are that the multiple integrations are reduced by one order, the singularity is removed from the integral kernel, and no additional discretization in the vicinity of the region of interest is required.

Effect of temperature variation on the plate-end debonding of FRP-strengthened beams: A theoretical study

2021 ◽  
pp. 136943322110463
Author(s):  
Dong Guo ◽  
Wan-Yang Gao ◽  
Dilum Fernando ◽  
Jian-Guo Dai
Keyword(s):  
Temperature Variation ◽  
Thermal Loading ◽  
Closed Form Solution ◽  
Form Solution ◽  
Effect Of Temperature ◽  
Shear Stresses ◽  
Limited Information ◽  
Element Analysis ◽  
Bond Slip ◽  
Loading Effects

Steel/concrete structures strengthened with externally bonded FRP plates may be subjected to significant temperature variations during their service time. Such temperature variation (i.e., thermal loading) may significantly influence the debonding mechanism in FRP-strengthened structures due to the thermal incompatibility between the FRP plate and the substrate as well as the temperature-induced bond degradation at the FRP-to-steel/concrete interface. However, limited information is available on the effect of temperature variation on the debonding failure in FRP-strengthened beams. This paper presents a new and closed-form solution to investigate the plate-end debonding failure of the FRP-strengthened beam subjected to combined thermal and mechanical (i.e., flexural) loading. A bilinear bond-slip model is used to describe the bond behavior of the FRP-to-substrate interface. The analytical solution is validated through comparisons with finite element analysis results regarding the distributions of the interfacial shear stresses, the interfacial slips and the axial stresses of the FRP plate. Given that a constant bond-slip relationship is adopted, it is observed that an increase in service temperature will lead to an increased interfacial slip at the plate end and consequently a reduced plate-end debonding load, and vice versa. Further parametric studies have indicated that the thermal loading effects become more significant when shorter and stiffer FRP plates are applied for strengthening.

Quasi-Static Stresses Due to Moving Temperature Discontinuity on a Plane Boundary

1966 ◽  
Vol 33 (4) ◽  
pp. 814-816 ◽  
Author(s):  
A. Jahanshahi
Keyword(s):  
Closed Form ◽  
Elastic Medium ◽  
Closed Form Solution ◽  
Form Solution ◽  
Plane Boundary ◽  
Heated Region ◽  
Plane State ◽  
Uniform Velocity ◽  
Temperature Discontinuity ◽  
Thermoelastic Theory

Closed-form solution is constructed to plane state of strain generated in a semi-infinite elastic medium when a portion of its boundary is heated. The heated region is assumed to be moving with uniform velocity. It is shown that stresses are bounded everywhere and are identically zero when the velocity of the moving temperature discontinuity vanishes. The study is based on uncoupled quasi-static thermoelastic theory.

Closed-Form Transient Response of Distributed Damped Systems, Part II: Energy Formulation for Constrained and Combined Systems

1996 ◽  
Vol 63 (4) ◽  
pp. 1004-1010 ◽  
Author(s):  
Bingen Yang
Keyword(s):  
Closed Form ◽  
Transient Response ◽  
Differential Operators ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Form Solution ◽  
Response Analysis ◽  
Lumped Parameter ◽  
Damped Systems ◽  
Energy Formulation

The transient response analysis presented in Part I is generalized for distributed damped systems which are viscoelastically constrained or combined with lumped parameter systems. An energy formulation is introduced to regain symmetry for the spatial differential operators, which is destroyed in the original equations of motion by the constraints, and the coupling of distributed and lumped elements. As a result, closed-form solution is systematically obtained in eigenfunction series.

A Circular Inclusion With Imperfect Interface: Eshelby’s Tensor and Related Problems

1995 ◽  
Vol 62 (4) ◽  
pp. 860-866 ◽  
Author(s):  
Zhanjun Gao
Keyword(s):  
Closed Form Solution ◽  
Subsequent Development ◽  
Physical Nature ◽  
Circular Inclusion ◽  
Imperfect Interface ◽  
Form Solution ◽  
Normal Displacement ◽  
Tangential Displacement ◽  
Shear Stresses ◽  
Eshelby’S Tensor

Eshelby’s tensor for an ellipsoidal inclusion with perfect bonding at interface has proven to have a far-reaching influence on the subsequent development of micromechanics of solids. However, the condition of perfect interface is often inadequate in describing the physical nature of the interface for many materials in various loading situations. In this paper, Airy stress functions are used to derive Eshelby’s tensor for a circular inclusion with imperfect interface. The interface is modeled as a spring layer with vanishing thickness. The normal and tangential displacement discontinuities at the interface are proportional to the normal and shear stresses at the interface. Unlike the case of the perfectly bonded inclusion, the Eshelby’s tensor is, in general, not constant for an inclusion with the spring layer interface. The normal stresses are dependent on the shear eigenstrain. A closed-form solution for a circular inclusion with imperfect interface under general two-dimensional eigenstrain and uniform tension is obtained. The possible normal displacement overlapping at the interface is discussed. The conditions for nonoverlapping are established.

Fractional Calculus Model of the Semilunar Heart Valve Vibrations

2003 ◽  
Author(s):  
Moustafa El-Shahed
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Numerical Methods ◽  
Fractional Calculus ◽  
Closed Form ◽  
Heart Valve ◽  
Laplace Transformation ◽  
Closed Form Solution ◽  
Equation Of Motion ◽  
Form Solution

The objective of this paper is to solve the equation of motion of semilunar heart valve vibrations. The vibrations of the closed semilunar valves were modeled with a Caputo hactional derivative of order α. With the help of Laplace transformation, closed-form solution is obtained for the equation of motion in terms of Mittag-Leffler function. An alternative Method for Semi-differential equation, when α = 0.5, is examined using MATHEMATICA. The simplicity of these solutions makes them ideal for testing the accuracy of numerical methods. This solution can be of some interest for a better fit of experimental data.

Motion of a Bored Sphere in a Spinning Spherical Cavity

1981 ◽  
Vol 103 (4) ◽  
pp. 389-394 ◽  
Author(s):  
R. H. Nunn ◽  
J. W. Bloomer
Keyword(s):  
Numerical Methods ◽  
Closed Form ◽  
Predictive Model ◽  
Spherical Cavity ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Form Solution ◽  
Analytical Expressions ◽  
Theory And Experiment

Theory and experiment are combined to develop a predictive model for the motion of a bored sphere within a spinning spherical cavity. The motion is gyroscopic in nature with the sphere eventually aligning its hole with the axis of spin of the cavity. Analytical expressions are derived for the applied moments on the sphere due to its motion relative to that of the cavity, and the resulting equations of motion are solved by numerical methods. An approximate closed-form solution is also obtained. Experiments are described in which the measured nutation of the sphere substantiates the analytical predictions.

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