Static analysis of beam structures under nonlinear geometric and constitutive behavior

This paper presents an analytical approach to investigate the non-linear axisymmetric response of functionally graded shallow spherical shells subjected to uniform external pressure incorporating the effects of temperature. Material properties are assumed to be temperature-independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and compatibility equations for shallow spherical shells are derived by using the classical shell theory and specialized for axisymmetric deformation with both geometrical non-linearity and initial geometrical imperfection are taken into consideration. One-term deflection mode is assumed and explicit expressions of buckling loads and load–deflection curves are determined due to Galerkin method. Stability analysis for a clamped spherical shell shows the effects of material and geometric parameters, edge restraint and temperature conditions, and imperfection on the behavior of the shells.

Non-linear axisymmetric response of functionally graded shallow spherical shells under uniform external pressure including temperature effects

An analytical approach for the sequential excavation of axisymmetric lined tunnels in viscoelastic rock

https://eprints.ncl.ac.uk/file_store/production/232634/94D19CB1-32DC-45CE-A40C-2CDE88C9E618.pdf

Analytical solutions of stresses and displacements for deeply buried twin tunnels in viscoelastic rock

The study intends to investigate the large amplitude vibration of functionally graded material (FGM) orthotropic cylindrical shells interacting with the nonlinear Winkler elastic foundation in the framework of the Donnell's shell theory is investigated. To derivation of basic equations of FGM orthotropic cylindrical shells interacting with the nonlinear elastic foundation is used von-Karman type geometric nonlinearity. The superposition and Galerkin methods are used to convert the above equations into a nonlinear ordinary differential equation. The frequency-amplitude characteristics of functionally graded (FG) orthotropic cylindrical shell interacting with the nonlinear elastic foundation are obtained using the semi-inverse method. The accuracy of the current study is verified by comparing it other solutions available in the literature. Moreover, some new results are also presented for the nonlinear frequency parameters of the cylindrical shells to study the effects of the nonlinear elastic foundation, vibration amplitude, FG orthotropic profiles and shell characteristics.

Large amplitude vibration of FGM orthotropic cylindrical shells interacting with the nonlinear Winkler elastic foundation

Buckling analysis of variable angle tow composite plates with a through-the-width or an embedded rectangular delamination

Non-uniform eigenstrain induced stress field in an elliptic inhomogeneity embedded in orthotropic media with complex roots

An analytical solution is developed in this paper for viscoelastic axisymmetric plane problems under stress or displacement boundary condition involving time-dependent boundary regions using the Laplace transform. The explicit expressions are given for the radial and circumferential stresses under stress boundary condition and the radial displacement under displacement boundary condition. The results indicate that the two in-plane stress components and the displacement under corresponding boundary conditions have no relation with material constants. The general form of solutions for the remaining displacement or stress field is expressed by the inverse Laplace transform concerning two relaxation moduli. As an application to deep excavation of a circular tunnel or finite void growth, explicit solutions for the analysis of a deforming circular hole in both infinite and finite planes are given taking into account the rheological characteristics of the rock mass characterized by a Boltzmann or Maxwell viscoelastic model. Numerical examples are given to illustrate the displacement and stress response. The method proposed in this paper can be used for analysis of earth excavation and finite void growth.

G. H. Nie

Papers

Buckling analysis of variable angle tow composite plates with a through-the-width or an embedded rectangular delamination

Non-uniform eigenstrain induced stress field in an elliptic inhomogeneity embedded in orthotropic media with complex roots

Analytical expressions for stress and displacement fields in viscoelastic axisymmetric plane problem involving time-dependent boundary regions

Asymptotic buckling analysis of imperfect shallow spherical shells on non-linear elastic foundation

Application of rayleigh-Ritz formulation to thermomechanical buckling of variable angle tow composite plates with general in-plane boundary constraint