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The non-linear response of a sandwich panel with the core that consists of a functionally graded material (FGM) undergoing in-plane loading is investigated. The panel consists of two face sheets, metallic or composite laminated, and an FGM core that is a medium whose mechanical properties change through the depth facilitating a desirable response of the structure. The effect of the FGM core is introduced through the constitutive relations that affect conventional and high-order stress resultants and stress couples in the panel. The formulation employs the Extended High-Order Sandwich Panel Theory (EHSAPT) to assess the effect of the FGM material of the core. A variational approach is adopted to derive the linear and non-linear governing equations with a prescribed FGM distribution through the depth of the core. The wrinkling study of FGM panels includes two loading scenarios where in-plane loads are applied through a rigid edge beam connected to the core only and where the loads are applied through a rigid edge structure attached to both the face sheets and core causing uniform end shortening. The post-wrinkling behavior is also considered to prove that the initial pattern of wrinkles is not affected.

On the basis of the two-dimensional theory of anisotropic thermoelasticity, a solution is given for the thermal stress intensity factors due to the obstruction of a uniform heat flux by an insulated line crack in a generally anisotropic half plane. The crack is replaced by continuous distributions of sources of temperature discontinuity and dislocations. First, the particular thermoelastic dislocation solutions for the half plane are obtained; then the corresponding isothermal solutions are superposed to satisfy the traction-free conditions on the crack surfaces. The dislocation solutions are applied to calculate the thermal stress intensity factors, which are validated by the exact solutions. The effects of the uniform heat flux, the ply angle and the crack length are investigated.

Thermal fields may exist in addition to mechanical loading, for example, due to short term exposure to fire. In this paper, the branching of cracks in the presence of combined thermal and mechanical loads is investigated for general anisotropic media by employing the theory of Stroh’s dislocation formalism, extended to thermo-elasticity in matrix notation. A general solution to the thermo-elastic crack problem for an anisotropic material under arbitrary loading is obtained in a compact form. Green’s functions are also presented for a thermal dislocation (heat vortex) and a conventional dislocation (or, referred as mechanical dislocation), which are formulated considering the cuts located at an arbitrary angle with respect to the x1 axis of the coordinate system (x1, x2, x3). Using the derived compact expressions, the interaction between the crack and the dislocation is studied and a closed form solution for this interaction is obtained. The branching portion of the thermo-elastic crack is modelled as a continuous distribution of dislocations. This problem is then converted into a set of singular integral equations. Numerical results are presented to illustrate the possible effects of thermal loading on the propagation of the branched crack.

A closed form elastodynamic solution for the thermal shock stresses due to heat transfer into/from a medium (e.g. fluid) at a constant temperature in a thick orthotropic cylindrical shell is developed. Temperature distribution varies with time and space throughout the shell thickness. The mathematical formulation is done by the three-dimensional linear dynamic elasticity approach and the use of appropriate integral transforms such as the finite Hankel transform and the Laplace transform. No restrictions are imposed regarding the shell thickness in the formulation. The present case, which is more practical and general, is an extension of the case of uniform heating previously studied by the authors. Numerical results show the role of the stress wave propagation and reflection in conjunction with the thermal and material orthotropy. These have a significant influence on the dynamic thermal shock stresses through the shell thickness. Results present the complete dynamic response of thermal shock stresses using realistic inertia parameters and material properties in a thick orthotropic cylindrical shell made out of glass/epoxy.

The objective of this paper is to answer the question of how accurately the simple Euler or transverse shear correction Engesser/Haringx/Timoshenko column buckling formulae are, when orthotropic composite material and moderate thickness are involved. The column is in the form of a hollow circular cylinder and the Euler or Timoshenko loads are based on the axial modulus. For this purpose, a three-dimensional elasticity solution is presented. As an example, the cases of an orthotropic material with stiffness constants typical of glass/epoxy or graphite/epoxy and the reinforcing direction along the periphery or along the cylinder axis are considered. First, it is found that the elasticity approach predicts in all cases a lower than the Enter value critical load. Moreover, the degree of non-conservatism of the Euler formula is strongly dependent on the reinforcing direction; the axially reinforced columns show the highest deviation from the elasticity value. The degree of non-conservatism of the Euler load for the circumferentially reinforced columns is much smaller and is comparable to that of isotropic columns. Second, the Engesser or first Timoshenko shear correction formula is in all cases examined conservative, i.e., it predicts a lower critical load than the elasticity solution. The Haringx or second Timoshenko shear correction formula is in most cases (but not always) conservative. However, in all cases considered, the second estimate is always closer to the elasticity solution than the first one. For the isotropic case both Timoshenko formulas are conservative estimates. Examination of a new formula for column buckling that adds a second term to the Euler load expression and is supposed to account for thickness effects, shows that this estimate is a non-conservative estimate but performs very well with very thick sections, being closest to the elasticity solution, but in general no better than the Timoshenko formulas for moderate thickness.

A formulation based on the three dimensional theory of elasticity is employed to study the buckling of an orthotropic cylindrical shell under external pressure. In this paper, a non-zero axial displacement and a full dependence of the buckling modes on the three coordinates is assumed, as opposed to the ring approximation employed in the earlier studies. The results from this elasticity solution are compared with the critical loads predicted by the orthotropic Donnell and Timoshenko non-shallow shell formulations. Two cases of end conditions are considered; one with both ends of the shell fixed, and the other with both ends capped and under the action of the external pressure. Moreover, two cases of orthotropic material are considered with stiffness constants typical of glass/epoxy and graphite/epoxy. For the isotropic material case, the predictions of the simplified (single expression) Donnell and the Flugge and the Danielson and Simmonds theories are also compared. In all cases, the elasticity approach predicts a lower critical load than the shell theories, the percentage reduction being larger with increasing thickness. The degree of non-conservatism depends strongly on the material properties, being smaller for the isotropic case. Furthermore, although it is a commonly accepted notion that the critical point in loading under external pressure occurs for n = 2 and m = 1 (number of circumferential waves and number of axial half-waves, respectively), it was found that this is not the case for the strongly orthotropic graphite/epoxy material and the moderately thick construction; for this case, the value of m at the critical point is greater than 1 (yet, in all cases n = 2).

The analytical solution for the stress field is derived for the case of a non-homogeneous curved beam in the form of a segment of a plane circular ring fixed at one end and acted upon by a load at the other end. It is assumed that the beam possesses general anisotropy and that the elastic constants are linear functions (with two non-zero coefficients) of the radial distance. The solution is found in a series form with a complex stress function. Numerical examples for the distribution of stresses in comparison with the homogeneous orthotropic case are presented and the effect of the gradient in the elastic constants is discussed.

The problem of obtaining the thermal stresses and displacements in an orthotropic elliptic cylinder (as can be produced by filament winding on a mandrel of elliptical cross-section) due to a uniform change in temperature, is formulated. The material properties are assumed to be independent of temperature and the anisotropy is referred to the coordinate system that is inherent to the geometry of the filament wound body. A displacement approach is used. Illustrative results are presented for the distribution of stresses and displacements in these orthotropic cylindrical tubes of elliptic cross-section and a comparison with the limit of circular hollow cylinders is made.

This paper provides a method for obtaining the mixed-mode stress intensity factors for a bi-material interface crack in the infinite strip configuration and in the case where both phases are fully anisotropic. First, the dislocation solution in a bi-material anisotropic infinite strip is investigated (the boundary of the strip is parallel to the bi-material interface). A surface distributed dislocation approach is employed to ensure the traction-free conditions at the strip bounding surfaces. Subsequently, the derived dislocation solution is applied to calculate the mixed-mode stress intensity factors of a crack located at, or parallel to, the interface in the bi-material anisotropic infinite strip. The crack itself is modelled as a distribution of the derived dislocation solutions for the strip. Results are presented and the effects of material mismatch, the length of the crack and the material interface on the stress intensity factors are investigated.

Crack initiation and early growth in asymmetric fully plastic plane strain configurations in power-law hardening materials is investigated numerically via the finite element method. In such asymmetric configurations a single shear band is present instead of the two shear bands of the symmetric case. Results for two strain hardening exponents, n = 0.12 and n = 0.24, indicate that cracking occurs at an angle of 39–43° from the transverse, smaller than 45° due to the higher triaxiality. The direction of cracking is closer to 45° for lower strain hardening exponents and is within 2° of experimental values. The stress and strain field is consistent with the singular power-law, extended for Mixed Modes I and II, HRR fields. The far-field displacement vector is not along the shear band but at about 68–70° from the transverse at initiation, indicating the presence of a Mode I component. Early growth, studied by successive removal of elements reaching unit damage, results in a crack growth per unit displacement for the lower hardening case of about twice that of the higher hardening one.