STRESS CHARACTERIZATION OF NONISOTHERMAL ELASTODYNAMICS FOR NONHOMOGENEOUS ANISOTROPIC BODY UNDER PLANE STRAIN CONDITIONS

摘要

Stress characterization of non-isothermal elastodynamics for an anisotropic nonhomogeneous infinite cylinder under plane strain conditions is presented. The cylinder is referred to the Cartesian coordinates x(i) (i = 1, 2, 3) in which the axis of the cylinder is parallel to the x(3)-axis and a cross-section of the cylinder at x(3) = 0, denoted by C, is a domain of the time-dependent stresses S-ij = S-ij(x(alpha), t), [i, j = 1, 2, 3; alpha = 1, 2; x(alpha) is an element of C; t >= 0]. The density of the cylinder rho, the compliance tensor K-ijkl [i, j, k, l = 1, 2, 3], and the stress-temperature tensor M-ij depend on x(2) only, while a thermomechanical load that complies with the plane strain conditions, depends on (x(1), x(2)) is an element of C and time t >= 0 only. It is shown that S-ij = S-ij(x(alpha), t) is generated by a unique solution S-alpha beta = S-alpha beta(x(gamma), t), [alpha, beta, gamma = 1, 2; t >= 0] to a pure stress initial-boundary value problem of nonisothermal elastodynamics on C x [0, infinity), and the in-plane stress components S-alpha beta - S-alpha beta((A)) generate the out-of plane stress components S-i3 - S-i3((A)), [i = 1, 2, 3] provided the inner product of a compliance dependent tensor field kappa((i)(alpha beta)) = kappa((i)(alpha beta)) (x(2)) and the tensor S-alpha beta - S-alpha beta((A)) does not vanish; here, S-ij(A) = S-ij(A) (X-alpha, t), [i, j = 1, 2, 3; alpha = 1, 2; x(alpha) is an element of C; t >= 0] represents the actuation tensor field. Also, a body-force analogy for S-alpha beta = S-alpha beta(x(gamma), t) is formulated from which it follows that S-alpha beta = S-alpha beta(x(gamma), t) can be identified with a solution to a pure stress initial-boundary value problem of isothermal elastodynamics. The stress characterization presented here should prove useful in a study of stress waves in an infinite cylinder made of an anisotropic functionally graded material within both the isothermal and non-isothermal elastodynamics.