Extended superconformal higher-spin gauge theories in four dimensions

Using the off-shell formulation for $$ \mathcal{N} $$ N = 2 conformal supergravity in four dimensions, we describe superconformal higher-spin multiplets of conserved currents in a curved background and present their associated unconstrained gauge prepotentials. The latter are used to construct locally superconformal chiral actions, which are demonstrated to be gauge invariant in arbitrary conformally flat backgrounds. The main $$ \mathcal{N} $$ N = 2 results are then generalised to the $$ \mathcal{N} $$ N -extended case. We also present the gauge-invariant field strengths for on-shell massless higher-spin $$ \mathcal{N} $$ N = 2 supermultiplets in anti-de Sitter space. These field strengths prove to furnish representations of the $$ \mathcal{N} $$ N = 2 superconformal group.

Impact of Material Stiffness and Anisotropy on Coaptation Characteristics for Aortic Valve Cusps Reconstructed from Pericardium

The numerical assessment of reconstructed aortic valves competence and leaflet design optimization rely on both coaptation characteristics and the diastolic valve configuration. These characteristics can be evaluated by the shell or membrane formulations. The membrane formulation is preferable for surgical aortic valve neocuspidization planning since it is easy to solve. The results on coaptation zone sensitivity to the anisotropy of aortic leaflet material are contradictive, and there are no comparisons of coaptation characteristics based on shell and membrane models for anisotropic materials. In our study, we explore for the first time how the reduced model and anisotropy of the leaflet material affect the coaptation zone and the diastolic configuration of the aortic valve. To this end, we propose the method to mimic the real, sutured neo-leaflet, and apply our numerical shell and membrane formulations to model the aortic valve under the quasi-static diastolic pressure varying material stiffness and anisotropy directions. The shell formulation usually provides a lesser coaptation zone than the membrane formulation, especially in the central zone. The material stiffness does influence the coaptation zone: it is smaller for stiffer material. Anisotropy of the leaflet material does not affect significantly the coaptation characteristics, but can impact the deformed leaflet configuration and produce a smaller displacement.

Properties of an Alternative Off-Shell Formulation of 4D Supergravity

This article elaborates on an off-shell formulation of D = 4, N = 1 supergravity whose auxiliary fields comprise an antisymmetric tensor field without gauge degrees of freedom. In particular, the relation to new minimal supergravity, a supercovariant tensor calculus and the construction of invariant actions including matter fields are discussed.

A nonlinear rotation-free shell formulation with prestressing for vascular biomechanics

We implement a nonlinear rotation-free shell formulation capable of handling large deformations for applications in vascular biomechanics. The formulation employs a previously reported shell element that calculates both the membrane and bending behavior via displacement degrees of freedom for a triangular element. The thickness stretch is statically condensed to enforce vessel wall incompressibility via a plane stress condition. Consequently, the formulation allows incorporation of appropriate 3D constitutive material models. We also incorporate external tissue support conditions to model the effect of surrounding tissue. We present theoretical and variational details of the formulation and verify our implementation against axisymmetric results and literature data. We also adapt a previously reported prestress methodology to identify the unloaded configuration corresponding to the medically imaged in vivo vessel geometry. We verify the prestress methodology in an idealized bifurcation model and demonstrate the significance of including prestress. Lastly, we demonstrate the robustness of our formulation via its application to mouse-specific models of arterial mechanics using an experimentally informed four-fiber constitutive model.

Study of the effects of shear piezoelectric actuators on the performance of laminated composite shells by an isogeometric approach

This paper presents an isogeometric approach based on the Non-Uniform Rational B-Splines (NURBS) to investigate static and free vibration responses of smart composite shells integrated with shear piezoelectric actuators. The degenerated shell formulation according to the Mindlin-Reissner shell theory is combined with the isogeometric approach. To model the laminated smart shells, the Equivalent Single Layer (ESL) theory is used. To consider the electric potential in the shear piezoelectric actuator layers, a sub-layer approach is adopted that assumes linear variation in the thickness direction of the sub-layer. The effect of different mechanical and electrical boundary conditions on transverse deformation and natural frequencies of laminated smart shells by applying the electric field have been investigated. In the case studies, two parallel edges of the considered shell structures are assumed simply supported and the other two with an arbitrary combination of boundary conditions including clamped, free or simply supports. Also, open-circuit and closed-circuit conditions are used as electric boundary conditions. Investigation of the effects of the shear piezoelectric actuator layers on various factors, including the simultaneous mechanical and electrical loadings as well as the radius of curvature of the shell are amongst the objects of this paper. Also, several numerical examples are presented to demonstrate the efficiency and accuracy of the isogeometric approach in the study of shear effects of the piezoelectric actuator layers. The obtained results indicate the reliability and desirability of the proposed approach.

3-D Integral Formulation for Thin Electromagnetic Shells Coupled with an External Circuit

The aim of this article is to present a hybrid integral formulation for modelling structures made by conductors and thin electromagnetic shell models. Based on the principle of shell elements, the proposed method provides a solution to various problems without meshing the air regions, and at the same time helps to take care of the skin effect. By integrating the system of circuit equations, the method presented in this paper can also model the conductor structures. In addition, the equations describing the interaction between the conductors and the thin shell are also developed. Finally, the formulation is validated via an axisymmetric finite element method and the obtained results are compared with those implemented from another shell formulation.

Investigation on Vibration Response for Misaligned Rotor-Bearing-Flexible Disc Coupling System—Theory and Experiment

Modeling of the dynamic behavior of the rotating system when subject to misaligned shafts is an interesting subject, aiming either the selection of appropriate couplings from early stages of project or the monitoring and model-based diagnosis of such machines. This research is focused on the dynamics of the system when angular misalignment is induced. The methodology to take into account this fault is based on the structural analysis of the flexible coupling, with the consequent use of cyclic restoring forces and moments exerted by this component on the coupled shafts. Structural analysis of metallic disc coupling is conducted by means of the finite element method, in which the flexible disc component is modeled using thin shell formulation. Once misalignments are applied, the cyclic nature of coupling efforts is captured by the application of consecutive shaft spin angles. Steady-state response is simulated and then displacements spectrum are analyzed in order to highlight harmonic components rising due to misalignment. Test rig measurements are performed, and the theoretical model is discussed in terms of locus, frequency response function (FRF), orbit shape, and spectrum information. Disc coupling is regarded, as limited literature in vibration spectrums is available for this type of coupling.