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

p-Extension of C-0 continuous mixed finite elements for plane strain gradient elasticity

A MIXED FINITE ELEMENT FORMULATION is developed for the general 2D plane strain, linear isotropic gradient elasticity problem. Form II of the dipolar strain gradient theory for micro-structured solids is considered. The main variables are the double stress tensor mu and the displacement field vector u. Standard C-0-continuous, high polynomial order hierarchical basis functions are employed for the finite element solution spaces (p-extension). The formulation is numerically validated against the standard axial tension patch test and the Mode I crack problem. The theoretical convergence rates of the uniform h- and p-extensions are confirmed using a benchmark problem where only double stresses appear. Results for the crack problem demonstrate that proper mesh refinement at areas of steep gradients ensures reproduction of the exact solution behaviour at different length scales. More specifically, the asymptotic exponents of the crack face opening displacement and the crack head true stress solutions of the Mode I crack problem are recovered. Finally, the upper bound of the true tensile normal stress near the crack tip is estimated. This upper bound is of major importance since the nature of the exact solution may change radically as we proceed from the macro- to micro-scale

Convergence and performance of the h- and p-extensions with mixed finite element C0-continuity formulations, for tension and buckling of a gradient elastic beam

AbstractMixed formulations with C0-continuity basis functions are employed for the solution of some types of one-dimensional fourth- and sixth-order equations, resulting from axial tension and buckling of gradient elastic beams, respectively. A basic characteristic of gradient elasticity type equations is the appearance of boundary layers in the higher-order derivatives of the displacements (e.g., in the stress fields). This is due to the small parameters (related to the size of the microstructure) entering the governing equations. The proposed mixed formulations are based on generalizations of the well-known Ciarlet–Raviart mixed method, where the new main variables are related to second-order (or fourth order, for the buckling problem) derivatives of the displacement field. The continuous and discrete Babuška–Brezzi inf–sup conditions are established. The mixed formulations are numerically tested for both the uniform h- and p-extensions. With regard to the axial tension problem, the standard quasi-optimal rates of convergence are numerically verified in all cases (i.e., algebraic rate of convergence for the h-extension and exponential rate for the p-extension). On the other hand, the h-extension observed convergence rates of the critical (buckling) load for the second model problem are slightly higher than the theoretical ones found in the literature (especially for polynomial order p=1). The respective observed rates of convergence of the buckling load for the p-extension are still exponential

Finite element predictions on vibrations of laminated composite plates incorporating the random orientation, agglomeration, and waviness of carbon nanotubes

In the present article, the vibration analysis of laminated composite plates strengthened with multi-walled carbon nanotubes (MWCNTs) is performed, employing the finite element method. Rule of mixtures and the Halpin–Tsai model are utilized to ascertain the elastic properties of the nanocomposite matrix. The effect of random orientation, the curved state, and the agglomeration of carbon nanotubes in the epoxy resin on mechanical properties is investigated. Classical lamination theory is also implemented to theoretically estimate the natural frequencies for validation purposes. Then, the natural frequencies of the laminated composite plates are determined by the numerical method for various parameters involved in the design process. The effect of MWCNTs’ inclusion on the natural frequencies of the carbon nanotube-based laminated plate, taking into account the reformed micromechanical Halpin–Tsai model, is finally investigated. The outcomes of the research are in compliance with experimental values and theoretical evidence available in the bibliography. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature

Gradient elasticity

Abstract. A mixed formulation with two main variables, based on the Ciarlet-Raviart technique, with