Time-dependent creep stress redistribution analysis of thick-walled FGM spheres subjected to an internal pressure and a uniform temperature field is investigated. The material creep and mechanical properties through the radial graded direction are assumed to obey the simple power-law variation throughout the thickness. Total strains are assumed to be the sum of elastic, thermal and creep strain...

In this paper, we present a general model for predicting the fatigue behavior for any stress level and amplitude using the exponential model. Based on the W\"ohler field for fixed stress level, a compatibility functional equation enables us to derive the general model with eight parameters. The problem of parameter estimation is then

We prove that the quasiregular mappings given by the (normalized) principal solution of the linear Beltrami equation (1) and the principal solution of the quasilinear Beltrami equation are inverse to each other. This basic fact is deduced from the Liouville theorem for generalized analytic functions. It essentially simplifies the known proofs of the “measurable Riemann mapping theorem” and its ...

The Laplace–Beltrami operator, a fundamental object associated with Riemannian manifolds, encodes all intrinsic geometry of manifolds and has many desirable properties. Recently, we proposed the point integral method (PIM), a novel numerical method for discretizing the Laplace–Beltrami operator on point clouds (Li et al. in Commun Comput Phys 22(1):228–258, 2017). In this paper, we analyze the ...

We estimate the Hölder exponent α of solutions to the Beltrami equation ∂f = μ∂f , where the Beltrami coefficient satisfies ‖μ‖∞ < 1. Our estimate improves the classical estimate α ≥ ‖Kμ‖ , where Kμ = (1 + |μ|)/(1 − |μ|), and it is sharp, in the sense that it is actually attained in a class of mappings which generalize the radial stretchings. Some other properties of such mappings are also prov...

Recently, certain higher dimensional complex manifolds were obtained in [1] by associating a higher dimensional uniformisation to the generalised Teichmüller spaces of Hitchin. The extra dimensions are provided by the “times” of the generalised KdV hierarchy. In this paper, we complete the proof that these manifolds provide the analog of superspace for W-gravity and that Wsymmetry linearises on...

Following Bojarski and Vekua, we have studied the Dirichlet problem $$ \underset{z\to \zeta }{\lim}\operatorname{Re}\ f(z)=\varphi \left(\zeta \right) as z ? ?, ? D, ? ?D, with continuous boundary data ?(?) in bounded domains D of complex plane ?, where f satisfies degenerate Beltrami equation {f}_{\overline{z}}=\mu (z){f}_z,\left|\mu (z)\right|<1 , a.e. D. Assuming that is an arbitrary simply ...

We study harmonic maps between surfaces, that are solutions to a nonlinear elliptic PDE. In Refs. Minsky (1992); Wolf (1989) it was proved diffeomorphisms, with nonvanishing Hopf differential, satisfy Beltrami equation of certain type: the imaginary part logarithm coefficient coincides differential. Therefore, is function. The real satisfies an differential equation, which in case constant curv...