Naobumi Sumi

Thermal stress singularities at tips of a Griffith crack in a finite rectangular plate

Abstract This paper is concerned with a method for calculating the thermal stresses in a finite rectangular plate with a Griffith crack under a steady state temperature field. In the analysis, based on the complex variable method for determining the stationary two-dimensional thermal stresses, the analytic continuation and the modified mapping-collocation methods are effectively employed. Numerical calculations for the strength of thermal stress singularity of the symmetric and the skew-symmetric types are carried out, and the results are shown in graphs.

TRANSIENT THERMAL STRESSES DUE TO A LOCAL SOURCE OF HEAT MOVING OVER THE SURFACE OF AN INFINITE ELASTIC SLAB

Abstract A solution is given for the transient thermal stresses due to a local source of heat that moves at constant speed over the surface of an infinite elastic slab. The transient temperature distribution is obtained by means of the Fourier and Laplace transforms, and the associated thermal stresses are obtained by making use of the thermoelastic displacement function and the Galerkin function.

STRESS INTENSITY FACTOR FOR TRANSIENT THERMAL STRESS OF A THIN PLATE WITH A GRIFFITH CRACK

A solution is given for the transient thermal stresses due to a Griffith crack in a thin plate. It is assumed that the transient thermal stress is set up by the application of the prescribed temperature at the crack surface and the heat exchange by the convection on the flat surfaces. By the use of the finite difference method for a time variable, an analytical solution for spatial variables can be obtained.

NUMERICAL SOLUTIONS OF THERMOELASTIC WAVE PROBLEMS BY THE METHOD OF CHARACTERISTICS

This article is concerned with the numerical treatment of thermal and thermal stress waves in thermoelastic solids. To keep the numerical treatment general, the development of the formulation is based on the generalized theory of thermoelasticity. A number of thermoelastic wave problems, which involve one or two space variables, are treated, in a uniform manner, by a system of first-order partial differential equations with stress, velocity, heat flow, and temperature as dependent variables. This system of equations is analyzed by the method of characteristics, yielding the characteristics and the characteristic equations. Procedures of numerical integration along the characteristics are established and carried out for several generalized and classical thermoelastic wave problems in homogeneous materials, composite materials, nonhomogeneous materials, and nonlinear elastic solids.

The propagation and reflection of thermal stress waves in anisotropic nonhomogeneous hollow cylinders and spheres

Abstract The propagation and reflection of thermal stress waves in anisotropic nonhomogeneous hollow cylinders and spheres subjected to radially symmetric time-dependent temperature fields are investigated. The material of the structure is assumed to be orthotropic with cylindrical or spherical anisotropy and, in addition, is continuously nonhomogeneous with thermal and mechanical properties varying along the radius. The curvilinear characteristics in the space-time plane are transformed into straight lines of equal slope so that the numerical errors can be minimized. The problem is then solved using appropriate characteristic relations on boundaries while using more convenient explicit finite-difference approximations at all other intermediate points in the transformed space-time plane. The physically interesting problem of an anisotropic nonhomogeneous hollow cylinder subjected to sudden uniform change in temperature of its internal boundary is considered in detail. The numerical results for the dynamic thermal stresses are shown in figures, and the effects of anisotropic nonhomogeneous material properties on the dynamic thermal stresses are discussed briefly.

SOLUTION FOR THERMAL AND MECHANICAL WAVES IN A PIEZOELECTRIC PLATE BY THE METHOD OF CHARACTERISTICS

The object of this article is to study the one-spatial dimensional thermal and mechanical waves in a piezoelectric infinite plate subjected to thermal, electric, and mechanical loadings. Based on the coupled generalized theory of piezothermoelasticity along with the modified Fourier law, the governing equations are expressed by a set of first-order partial differential equations with stress, particle velocity, electric field intensity, heat flow, and temperature as the unknown variables. This system of equations is analyzed by the method of characteristics. The numerical calculations are carried out for a traction-free PZT-4 plate subjected to impulsive surface heating. Graphical displays are utilized to present the outcome of the procedures.

Transient thermal stresses due to a zonal heat source moving back and forth over the surface on an infinite plate

Abstract A solution is given for the transient thermal stresses due to a zonal heat source moving back and forth with a constant angular frequency over the surface of an infinite elastic plate. The transient temperature distribution is obtained by using the complex Fourier and Laplace transforms, and the associated thermal stresses are obtained by means of the thermoelastic displacement potential and the Galerkin function. Graphical representations for the solution in dimensionless terms are included in this paper.

Thermal stresses in an orthotropic rectangular plate with a rigid ribbonlike inclusion

Abstract On the basis of the complex variable method for determining the stationary two-dimensional thermal stresses, the thermal stresses in an orthotropic rectangular plate with a rigid ribbonlike inclusion under a steady state temperature field is considered. The solution is found by the analytic continuation argument and the modified mapping-collocation technique. Numerical results indicate a dependence of the orthotropic stress intensity factors on the thermal, elastic and geometrical constants over a certain parameter range

Thermal Stresses in Beams

In this chapter, based on the Bernoulli-Euler hypothesis, thermal stresses in beams subjected to thermal and mechanical loads are recalled. Thermal stresses in composite and curved beams, and thermal deflections in beams subjected to a symmetrical thermal load are treated. Furthermore, solutions for stresses in curved beams are included. Problems and solutions for beams subjected to various temperature field or various boundary conditions are presented. [see also Chap. 23.]

THERMAL STRESSES IN A FINITE RECTANGULAR PLATE WITH A RIGID RIBBONLIKE INCLUSION

This paper provides a method for evaluating the thermal stresses in a finite rectangular plate with a rigid ribbonlike inclusion under a steady-state temperature field. In the analysis, based on the complex variable method for determining the stationary two-dimensional thermal stresses, the conformal mapping and analytic continuation arguments ensuring the mechanical boundary conditions on the inclusion are effectively employed. Numerical calculations for the strength of thermal-stress singularities of the symmetric type are carried out, and the results are shown in terms of the geometrical parameters.