T. K. Papathanasiou

A higher order FEM for time-domain hydroelastic analysis of large floating bodies in an inhomogeneous shallow water environment

The study of wave action on large, elastic floating bodies has received considerable attention, finding applications in both geophysics and marine engineering problems. In this context, a higher order finite-element method (FEM) for the numerical simulation of the transient response of thin, floating bodies in shallow water wave conditions is presented. The hydroelastic initial-boundary value problem, in an inhomogeneous environment, characterized by bathymetry and plate thickness variation, is analysed for two configurations: (i) a freely floating strip modelling an ice floe or a very large floating structure and (ii) a semi-fixed floating beam representing an ice shelf or shore fast ice, both under long-wave forcing. The variational formulation of these problems is derived, along with the energy conservation principle and the weak solution stability estimates. A special higher order FEM is developed and applied to the calculation of the numerical solution. Results are presented and compared against established methodologies, thus validating the present method and illustrating its numerical efficiency. Furthermore, theoretical results concerning the energy conservation principle are verified, providing a valuable insight into the physical phenomenon investigated.

Generalized Thermoelastic Models for Linear Elastic Materials with Micro-Structure Part I: Enhanced Green–Lindsay Model

In this article, we derive constitutive thermoelastic models for linear elastic materials with micro-structure. The elastic behavior is assumed to be consistent with Mindlins’ Form II gradient elasticity theory, whereas for the thermal behavior the generalization of Clausius-Duhem inequality, proposed by Green and Laws, is adopted. The resulting model is actually a generalization of the thermoelastic theory of Green and Lindsay for linear elastic materials with micro-structure, taking into account micro-inertia effects, as well. It is demonstrated that classical thermoelasticity models are retrieved from the present general formulation, when some of the model constants are set to zero. Finally, the uniqueness of solution for the general case of anisotropic materials is proved.

Generalized Thermoelastic Models for Linear Elastic Materials with Micro-Structure Part II: Enhanced Lord–Shulman Model

In this article, we derive constitutive thermoelastic models for linear elastic materials with micro-structure. The elastic behavior is assumed to be consistent with Mindlin Form II, whereas for the thermal behavior, the generalization of Fourier–Duhamel law proposed by Maxwell-Vernotte-Cattaneo is adopted. The resulting model is actually a generalization of the thermoelastic theory of Lord and Shulman, suitable for linear elastic materials with micro-structure taking into account micro-inertia effects as well. Uniqueness of the solution for the general case of anisotropic materials is proved. An application example is analyzed by means of the Finite Element method and comparisons are made with the generalized Green–Lindsay model derived in “Generalized Thermoelastic Models for Linear Elastic Materials with Micro-Structure Part I: Enhanced Green–Lindsay Model,” also in this issue.

Hydroelastic analysis of VLFS based on a consistent coupled-mode system and FEM

Three models for the interaction of water waves with large floating elastic structures are analysed. The first model, based on the Euler–Bernoulli beam theory, has already been extensively studied. The second is based on the Rayleigh beam equation. The third approach utilises the Timoshenko approximation and is thus capable of incorporating shear deformation and rotary inertia effects. A novelty of the proposed hydroelastic systems is the consistent local mode expansion of the underlying hydrodynamic field interacting with the floating structure, which leads to coupled-mode systems with respect to the modal amplitudes of the wave potential and the surface elevation. This representation is rapidly convergent to the solution of the full hydroelastic problem. The dispersion relations of these models are derived and analysed, supporting at a next stage the efficient development of finite element method solvers of the coupled system.

Wave reflection and transmission in multiply stented blood vessels

Closed circulatory systems display an exquisite balance between vascular elasticity and viscous fluid effects, to induce pulse-smoothing and avoid resonance during the cardiac cycle. Stents in the arterial tree alter this balance through stiffening and because a periodic structure is introduced, capable of interacting with the fluid in a complex way. While the former feature has been investigated, the latter received no attention so far. But periodic structures are the building blocks of metamaterials, known for their ‘non-natural’ behaviour. Thus, the investigation of a stents periodic microstructure dynamical interactions is crucial to assess possible pathological responses. A one-dimensional fluid–structure interaction model, simple enough to allow an analytical solution for situations of interest involving one or two interacting stents, is introduced. It is determined: (i) whether or not frequency bands exist in which reflected blood pulses are highly increased and (ii) if these bands are close to the characteristic frequencies of arteries and finally, (iii) if the internal structure of the stent can sensibly affect arterial blood dynamics. It is shown that, while the periodic structure of an isolated stent can induce anomalous reflection only in pathological conditions, the presence of two interacting stents is more critical, and high reflection can occur at frequencies not far from the physiological values.

Heat Transfer in Thin Multilayered Plates—Part I: A New Approach

We present a new model for the determination of temperature distributions in thin plates consisting of many different layers. The method uses both continuous and discrete approaches. The derived set of equations is based on a continuous representation of heat transfer phenomena at the midplane of each layer, whereas it facilitates a discrete process for introducing ply to ply, through thickness, heat transfer. For the steady state case, the resulting equations are of the Helmholtz type. Methods of solutions for the resulting system are discussed, and comparisons with the first order lamination theory are presented in a benchmark example. [.

On Vergnaud's time integration method for autocatalytic cure rate equations

A hybrid numerical-analytical scheme for time integration of the cure rate equation, governing the autocatalytic cure reaction of epoxy resins, is presented. The method is an extension of Vergnauds approach for the integration of heterocatalytic cure reactions of epoxy resins. It is applicable to first order, semi-linear, ordinary differential equations with separated variables, where the integration of the dependent variable can be obtained analytically. Numerical quadrature is used for the integration of the independent variable, which appears in a time-dependent integral of an Arrhenius term containing temperature. Consistency and L-stability of the method are proved and some error estimates are provided. Several numerical results validate the high accuracy of the proposed integration scheme.