On stability of stiffened cylindrical shells with varying material properties

The static stability analysis of stiffened functionally graded cylindrical shells by isotropic rings and stringers subjected to axial compression is presented in this paper. The Young's modulus of the shell is taken to be function of the thickness coordinate. The fundamental relations, the equilibrium and stability equations are derived using the Sander's assumption. Resulting equations are employed to obtain the closed-form solution for the critical axial loads. The effects of material properties, geometric size and different material coefficient on the critical axial loads are examined. The analytical results are compared and validated using the finite element model

Size-dependent nonlinear analysis of composite laminated micro skew plates reinforced with functionally graded graphene sheets

The high mechanical strength and superior physical properties of graphene and its derivatives have made them an ideal choice for modern engineering structures. The use of graphene as nanofillers in reinforced polymer composites has led to the development of sustainable high performance composite materials. Such materials can be utilized in engineering structures not only to improve their structural performance but also to reduce their environmental impact as well. Skew plates are commonly used in aerospace structures and ship hulls. In this paper, a size-dependent nonlinear model is presented for bending analysis of composite laminated micro skew plates reinforced with functionally graded graphene sheets. The modified Halpin-Tsai micromechanical model and rule of mixture are considered for the effective mechanical properties of graphene sheets which vary continuously throughout the thickness of the skew plate. The Schapery's model is considered for the effective thermal properties. The skew plate is assumed in thermal environments while transversely loaded. The governing equations of the problem are derived based on the Mindlin plate theory and the modified coupled stress theory. Using the generalised differential quadrature method, the nonlinear governing equations are first converted into a set of linear algebraic equations and then solved to obtain the bending moment of the skew plate under different loading conditions. Results show that reinforcing composite laminated micro skew plates with functionally graded graphene sheets increases the overall stiffness and bending strength of the plate, enhancing its performance under large deflections. It has also been observed that the bending performance of the skew plate further enhances through changing the distribution pattern of the functionally graded graphene reinforcement as well as with an increase in the angle of the skew plate

An efficient structural finite element for inextensible flexible risers

A core part of all numerical models used for flexible riser analysis is the structural component representing the main body of the riser as a slender beam. Loads acting on this structural element are self-weight, buoyant and hydrodynamic forces, internal pressure and others. A structural finite element for an inextensible riser with a point-wise enforcement of the inextensibility constrain is presented. In particular, the inextensibility constraint is applied only at the nodes of the meshed arc length parameter. Among the virtues of the proposed approach is the flexibility in the application of boundary conditions and the easy incorporation of dissipative forces. Several attributes of the proposed finite element scheme are analysed and computation times for the solution of some simplified examples are discussed. Future developments aim at the appropriate implementation of material and geometric parameters for the beam model, i.e. flexural and torsional rigidity

On thermo-mechanical nonlinear behaviour of shallow shells

The structural performance of thin shells is largely dictated by their curvature and the degree of lateral restraint at the shell edges. The present study is an attempt to theoretically investigate the influence of such factors on nonlinear thermo-mechanical response of shallow shells with single and double curvatures. For the mechanical loading, a transverse load is assumed and for the thermal loading, a through-depth thermal gradient is applied on the shallow shell. Two types of boundary conditions are considered for the shallow shell, both of which constrain transverse deflections of the shell but allow rotations parallel to the shell boundaries to be free. One of the boundary conditions permits lateral translation (laterally unrestrained) and the other one does not (laterally restrained). The fundamental nonlinear equations of shallow shells are derived based on the quasi-static conditions. The validity and reliability of the proposed approach is assessed by calculating several numerical examples for shallow shells under various mechanical and thermal loads. It is found that the proposed formulation, in particular, can adequately capture the nonlinear behaviour of laterally restrained shallow shells

Temperature-dependent nonlinear analysis of shallow shells: A theoretical approach

The paper presents a theoretical formulation for the computation of temperature-dependent nonlinear response of shallow shells with single and double curvatures subjected to transverse mechanical loads while being exposed to through-depth non-uniform heating regimes such as those resulting from a fire. The material nonlinearity arises from taking into consideration the degradation of the material elastic behaviour at elevated temperatures under quasi-static conditions. Two types of boundary conditions are considered, both of which constrain the transverse deflections and allow the rotations about the edge axis to be free. One of the boundary conditions permits lateral translation (laterally unrestrained) and the other one does not (laterally restrained). A number of examples are solved for shallow shells under different types of loading conditions including: an exponential "short hot" fire leading to a high temperature over a relatively short duration; and an exponential "long cool" fire of lower temperature over a longer duration. The limits of the shallow shell equations are investigated through comparison studies. Results show that while current numerical approaches for analysis of laterally restrained shallow shells are often computationally intensive, the proposed approach offers an adequate level of accuracy with a rapid convergence rate for such structures.The Edinburgh Research Partnership in Engineering (ERPE)