An Arbitrary Tangential Load Underneath a Smooth Circular Punch

1990 ◽  
Vol 57 (3) ◽  
pp. 596-599 ◽  
Author(s):  
V. I. Fabrikant
Keyword(s):  
Exact Solution ◽  
Transversely Isotropic ◽  
Elastic Half Space ◽  
Reciprocal Theorem ◽  
Tangential Load ◽  
Concentrated Load ◽  
Circular Punch ◽  
Angular Displacements ◽  
The Reciprocal Theorem ◽  
First Time

The problem of a smooth circular punch penetrating a transversely isotropic elastic half space and interacting with an arbitrarily located tangential concentrated load is considered. For the first time, a closed-form exact solution is obtained for the stress distribution under the punch as well as for the linear and angular displacements of the punch. The solution is based on the results previously obtained by the author and combined with the reciprocal theorem. A numerical example is presented as an illustration.

The Interaction Between a System of Circular Punches on an Elastic Half Space

1982 ◽  
Vol 49 (2) ◽  
pp. 341-344 ◽  
Author(s):  
G. M. L. Gladwell ◽  
V. I. Fabrikant
Keyword(s):  
Half Space ◽  
Approximate Solutions ◽  
Elastic Half Space ◽  
Concentrated Load ◽  
Circular Punch

Galin derived an expression for the pressure produced under a rigid circular punch by the application of a concentrated load at another point of the half space. This result is used to derive approximate relationships among the forces, moments, and indentations for a system of punches on an elastic half space. The results are compared with a number of earlier approximate solutions.

On Fundamental Solutions and Green’s Functions in the Theory of Elastic Plates

1966 ◽  
Vol 33 (1) ◽  
pp. 31-38 ◽  
Author(s):  
A. Kalnins
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Bessel Functions ◽  
Arbitrary Point ◽  
Fundamental Solutions ◽  
Addition Theorem ◽  
Reciprocal Theorem ◽  
Elastic Plates ◽  
Concentrated Load ◽  
The Reciprocal Theorem

This paper is concerned with fundamental solutions of static and dynamic linear inextensional theories of thin elastic plates. It is shown that the appropriate conditions which a fundamental singularity must satisfy at the pole follow from the requirement that the reciprocal theorem is satisfied everywhere in the region occupied by the plate. Furthermore, dynamic Green’s function for a plate bounded by two concentric circular boundaries is derived by means of the addition theorem of Bessel functions. The derived Green’s function represents the response of the plate to a harmonically oscillating normal concentrated load situated at an arbitrary point on the plate.

Nonuniformly Moving Loads on an Anisotropic Elastic Half-Space

2003 ◽  
Vol 19 (1) ◽  
pp. 217-224
Author(s):  
Kuang-Chong Wu
Keyword(s):  
Half Space ◽  
Moving Load ◽  
Constant Load ◽  
Elastic Half Space ◽  
Reciprocal Theorem ◽  
Line Load ◽  
Surface Displacements ◽  
Anisotropic Elastic ◽  
The Reciprocal Theorem ◽  
Rayleigh Wave Speed

ABSTRACTThe transient motion in an anisotropic elastic half-space due to a moving surface line load is considered. The load is applied suddenly on the surface and moves off in a fixed direction with nonuniform speed. Integral expressions for the displacements are derived using the reciprocal theorem. The waves generated by the moving load are discussed. Special attention is paid to the singularities in surface displacements generated as the load moves through the Rayleigh wave speed. Explicit expression is obtained for the particle velocity due to a constant load moving with constant speed.

Boundary Conditions for Axisymmetric Circular Cylinder of Cubic Quasicrystal

2010 ◽  
Vol 160-162 ◽  
pp. 204-209
Author(s):  
Bao Sheng Zhao ◽  
Yang Gao ◽  
Ying Tao Zhao
Keyword(s):  
Circular Cylinder ◽  
Boundary Conditions ◽  
Necessary Conditions ◽  
Reciprocal Theorem ◽  
Interior Solution ◽  
Analysis Technique ◽  
State Boundary ◽  
The Reciprocal Theorem ◽  
First Time ◽  
Correct Boundary Conditions

Through generalizing the method of a decay analysis technique determining the interior solution developed by Gregory and Wan, a set of necessary conditions on the end-data of axisymmetric circular cylinder in cubic quasicrystal for the existence of a rapidly decaying solution is established. By accurate solutions for auxiliary regular state, using the reciprocal theorem, these necessary conditions for the end-data to induce only a decaying elastostatic state (boundary layer solution) will be translated into appropriate boundary conditions for the circular cylinder with axisymmetric deformations in cubic quasicrystal. The results of the present paper enable us to establish a set of correct boundary conditions, and mix boundary conditions of which are obtained for the first time.

scholarly journals Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Seyyedeh Roodabeh Moosavi Noori ◽  
Nasir Taghizadeh
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Hybrid Technique ◽  
Transform Method ◽  
Proportional Delays ◽  
Differential Transform ◽  
Computational Work ◽  
Linear And Nonlinear ◽  
First Time

AbstractIn this study, a hybrid technique for improving the differential transform method (DTM), namely the modified differential transform method (MDTM) expressed as a combination of the differential transform method, Laplace transforms, and the Padé approximant (LPDTM) is employed for the first time to ascertain exact solutions of linear and nonlinear pantograph type of differential and Volterra integro-differential equations (DEs and VIDEs) with proportional delays. The advantage of this method is its simple and trusty procedure, it solves the equations straightforward and directly without requiring large computational work, perturbations or linearization, and enlarges the domain of convergence, and leads to the exact solution. Also, to validate the reliability and efficiency of the method, some examples and numerical results are provided.

scholarly journals Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 505-515 ◽  
Author(s):  
D. C. Gakenheimer ◽  
J. Miklowitz
Keyword(s):  
Exact Solution ◽  
Free Surface ◽  
Steady State ◽  
Wave Front ◽  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Point Load ◽  
Limit Case ◽  
Transient Waves

The propagation of transient waves in a homogeneous, isotropic, linearly elastic half space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are derived for the interior of the half space and for all load speeds. Wave-front expansions are obtained from the exact solution, in addition to results pertaining to the steady-state displacement field. The limit case of zero load speed is considered, yielding new results for Lamb’s point load problem.

Sign in / Sign up

Export Citation Format

Share Document