Thermoelasticity problem in a thick-walled cylinder is solved analytically using the finite Hankel transform. Timedependent thermal boundary conditions are assumed to act on the inner surface of the cylinder. For the mechanical boundary conditions two different cases are assumed: Traction-displacement problem (traction is prescribed on the inner surface and the fixed displacement boundary condition on the outer one) and Traction-Traction problem (tractions are prescribed on both the inner and outer surfaces of the hollow cylinder). The quasi-static solution of the thermoelasticity problem is derived analytically, i.e., the transient thermal response of the cylinder is derived and then, quasi-static structural problem is solved and closed form relations are extracted for the thermal stresses in the two problems. The results show to be in accordance with that cited in the literature in the special cases.
A B S T R A C T In this paper the method of weight functions is employed to calculate the stress intensity factors for an internal circumferential crack in a thick-walled cylinder. The pressurized cylinder is also subjected to convection cooling on the inner surface. Finite element method is used to determine an accurate weight function for the crack and a closed-form thermal stress intensity factor with the aid of the weight function method is extracted. The influence of crack parameter and the heat transfer coefficient on the stress intensity factors are determined. Comparison of the results in the special cases with those cited in the literature and the finite element data shows that the results are in very good agreement. a = crack depth a/t = relative depth Bi = Biot number h = convection coefficient H = material constant k = thermal conductivity K = stress intensity factor m(r, a) = weight function P i = internal pressure P o = external pressure R i = inner radius of cylinder R o = outer radius of cylinder t = cylinder wall thickness T i = initial temperature u = radial displacement v(a, x) = crack opening displacement Y 1 , Y 2 = boundary correction factors α = thermal conductivity μ = shear modulus of the material v = Poisson's ratio θ = temperature θ S = surrounding fluid temperature σ r = radial stress σ Z = axial stress Correspondence: R. Ghajar. E-mail: Ghajar@kntu.ac.ir †Post Doctoral Researcher
I N T R O D U C T I O NStructures with crack-like flaws require a thorough analysis in order to assess their load capacity, remaining service life, or level of safety. Cracks in pressure vessels often occur at welded joints, mostly located in the circumferential 504
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