Abstract

A general theory for the dynamic analysis of thin walled open beams taking into account shear deformability, variable cross-sectional properties and initial stresses is presented. The present approach, which is based on a general variational formulation of the theory of elasticity, allows the determination, in a unified fashion, of the governing unidimensional variatiotial equation of motion of the beam and the constitutive relations for the stress resultants. The niotion differential equations are then obtained. It is developed a finite element formulation based on the present theory, which is used for detemining natural frequencies of vibrations. Independent determinations are performed for sirriply supported thin walled open beams by means of an analytical solution of the present differential equations. Numerical experiments are done to show the importance of the considered effects and to assess the accuracy of the proposed finite element.

Abstract

A potential transonic solver with an embedded wake is presented. The flow outside of attached boundary layers of streamlined bodies flying at high Reynold numbers can be assumed to be irrotational and isentropic. This assumption reduces the NavierStokes equations to a single scalar nonlinear partial differential equation, namely the full-potential equation (FPE). The FPE expresses the conservation of mass in terms of the velocity potential. In this work, the FPE is discretized using a standard Galerkin finite element method, and the nonlinear system of equations stemming from the discretization is solved using Newton's method. An artificial compressibility method is used to stabilize the problem in supersonic flow regions. This method prevents the Jacobian from becoming singular and allows capturing shock waves. To include the viscosity effects in the lift generation, a model for the trailing wake needs to be introduced. In the presented method, the wake is modeled as a straight surface in the free-stream direction. This assumption is relaxed allowing mass flux across the wake. To capture the discontinuity in the velocity potential across the wake, a multivalued element method is employed.This implicit description of the wake within the mesh presents an effective approach to perform fluidstructure interaction computations and apply aeroelastic optimization methods, where the position of the wake changes during consecutive iterations. The solver is implemented in Kratos Multi-Physics and verified for different angles of attack and free-stream conditions. Since the pressure does not change in the transverse direction of the boundary layer, the FPE yields accurate lift, induced drag, and moment computations.

Abstract

This work describes a novel formulation for the simulation of Navier-Stokes problems including embedded objects. The new proposal is based on the use of a modified finite element space, which replaces the standard one within the elements intersected by the immersed geometry. The modified space is able to exactly reproduce the jumps happening at the embedded boundary while preserving the conformity across the faces intersected by the embedded object. The paper focuses particularly on the imposition of a slip boundary condition on the surface of the embedded geometry, proposing a new technique for the application of such constraint. The new proposal is carefully benchmarked using the results of a body fitted technique and of an alternative embedded approach. Potential applications of interest are also presented.

Abstract

This work explores the use of an embedded computational fluid dynamics method to study the type B aortic dissection. The use of the proposed technique makes it possible to easily test different intimal flap configurations without any need of remeshing. To validate the presented methodology, we take as reference test case an in vitro experiment present in the literature. This experiment, which considers several intimal flap tear configurations (number, size and location), mimics the blood flow in a real type B aortic dissection. We prove the correctness and suitability of the presented approach by comparing the pressure values and waveform. The obtained results exhibit a remarkable similarity with the experimental reference data. Complementary, we present a feasible surgical application of the presented computer method. The aim is to help the clinicians in the decision making before the type B aortic dissection surgical fenestration. The capabilities of the proposed technique are exploited to efficiently create artificial reentry tear configurations. We highlight that only the radius and center of the reentry tear need to be specified by the clinicians, without any need to modify neither the model geometry nor the mesh. The obtained computational surgical fenestration results are in line with the medical observations in similar clinical studies.

Abstract

This study presents a mixed finite element formulation able to address nearly-incompressible problems explicitly. This formulation is applied to elements with independent and equal interpolation of displacements and strains, stabilized by variational subscales (VMS). As a continuation of the study presented in reference [23], in which the strains sub-scale was introduced, in this work the effects of sub-scale displacements are included, in order to stabilize the pressure field. The formulation avoids the Ladyzhenskaya-Babuska-Brezzi (LBB) condition and only requires the solution of a diagonal system of equations. The main aspects of implementation are also discussed. Finally, numerical examples validate the behaviour of these elements compared with the irreductible formulation.

Abstract

This paper dels with the transverse vibration of non-uniform rotating beams, by means of the differential quadrature method (DQM). The formulation is based on the Timoshenko beam theory, wich takes into account the inertia forces due to the transverse translation together with the constributions of shear deformation and rotatory inertia. The application of the differential quadrature method is demostrated by investigating the natural frequencies. The results ara compared with published results given in the open literature and with values obtained by the authors using a finite element code. The proposed method offers a direct and efficient procedure to analyze the natural vibration of non-uniform rotating beams with very good accuracy.