32 research outputs found
Mixed Galerkin and least-squares formulations for isogeometric analysis.
Get PDFThis work is concerned with the use of isogeometric analysis based on Non- Uniform Rational B-Splines (NURBS) to develop efficient and robust numerical techniques to deal with the problems of incompressibility in the fields of solid and fluid mechanics. Towards this, two types of formulations, mixed Galerkin and least-squares, are studied. During the first phase of this work, mixed Galerkin formulations, in the context of isogeometric analysis, are presented. Two-field and three-field mixed variational formulations - in both small and large strains - are presented to obtain accurate numerical solutions for the problems modelled with nearly incompressible and elasto-plastic materials. The equivalence of the two mixed formulations, for the considered material models, is derived; and the computational advantages of using two-field formulations are illustrated. Performance of these formulations is assessed by studying several benchmark examples. The ability of the mixed methods, to accurately compute limit loads for problems involving elastoplastic material models; and to deal with volumetric locking, shear locking and severe mesh distortions in finite strains, is illustrated. Later, finite element formulations are developed by combining least-squares and isogeometric analysis in order to extract the best of both. Least-squares finite element methods (LSFEMs) based on the use of governing differential equations directly - without the need to reduce them to equivalent lower-order systems - are developed for compressible and nearly incompressible elasticity in both the small and finite strain regimes; and incompressible Navier-Stokes. The merits of using Gauss-Newton scheme instead of Newton-Raphson method to solve the underlying nonlinear equations are presented. The performance of the proposed LSFEMs is demonstrated with several benchmark examples from the literature. Advantages of using higher-order NURBS in obtaining optimal convergence rates for non-norm-equivalent LSFEMs; and the robustness of LSFEMs, for Navier-Stokes, in obtaining accurate numerical solutions without the need to incorporate any artificial stabilisation techniques, are demonstrated
A novel semi-implicit scheme for elastodynamics and wave propagation in nearly and truly incompressible solids
Get PDFThis paper presents a novel semi-implicit scheme for elastodynamics and wave propagation problems in nearly and truly incompressible material models. The proposed methodology is based on the efficient computation of the Schur complement for the mixed displacement-pressure formulation using a lumped mass matrix for the displacement field. By treating the deviatoric stress explicitly and the pressure field implicitly, the critical time step is made to be limited by shear wave speed rather than the bulk wave speed. The convergence of the proposed scheme is demonstrated by computing error norms for the recently proposed LBB-stable BT2/BT1 element. Using the numerical examples modelled with nearly and truly incompressible Neo-Hookean and Ogden material models, it is demonstrated that the proposed semi-implicit scheme yields significant computational benefits over the fully explicit and the fully implicit schemes for finite strain elastodynamics simulations involving incompressible materials. Finally, the applicability of the proposed scheme for wave propagation problems in nearly and truly incompressible material models is illustrated
Mixed displacementâpressure formulations and suitable finite elements for multimaterial problems with compressible and incompressible models
Get PDFMultimaterial problems in linear and nonlinear elasticity are some of the least explored using mixed finite element formulations with higher-order elements. The fundamental issue in adapting the mixed displacementâpressure formulations with linear and higher-order continuous elements for the pressure field is their inability to capture pressure and stress jumps across material interfaces. In this paper, for the first time in literature, we perform comprehensive studies of multimaterial problems in elasticity consisting of compressible and incompressible material models using the mixed displacementâpressure formulation to assess the performance of different element types in accurately resolving pressure fields within the domains and pressure jumps across material interfaces. In particular, infâsup stable displacementâpressure combinations with element-wise discontinuous pressure for triangular and tetrahedral elements are considered and their performance is assessed along with the Q1/P0 element and TaylorâHood elements using several numerical examples. The results show that TaylorâHood elements fail to capture the stress jumps due to the continuity of DOFs across elements, the CrouzeixâRaviart (P2b/P1dc) element yields substantially poor pressure fields despite a significant increase in pressure degrees of freedom and that the P3/P1dc element produces superior quality results fields when compared with the P2b/P1dc element
A comprehensive assessment of accuracy of adaptive integration of cut cells for laminar fluid-structure interaction problems
Get PDFFinite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are cut by the interface between two different domains need to be integrated using special techniques in order to obtain optimal convergence rates and accurate fluxes across the interface. The adaptive integration technique in which the cells are recursively subdivided is one of the popular techniques for the numerical integration of cut-cells due to its advantages over tessellation, particularly for problems involving complex geometries in three dimensions. Although adaptive integration does not impose any limitations on the representation of the geometry of immersed solids as it requires only point location algorithms, it becomes computationally expensive for recovering optimal convergence rates. This paper presents a comprehensive assessment of the adaptive integration of cut-cells for applications in computational fluid dynamics and fluid-structure interaction. We assess the effect of the accuracy of integration of cut cells on convergence rates in velocity and pressure fields, and then on forces and displacements for fluid-structure interaction problems by studying several examples in two and three dimensions. By taking the computational cost and the accuracy of forces and displacements into account, we demonstrate that numerical results of acceptable accuracy for FSI problems involving laminar flows can be obtained with only fewer levels of refinement. In particular, we show that three levels of adaptive refinement are sufficient for obtaining force and displacement values of acceptable accuracy for laminar fluid-structure interaction problems
A comprehensive assessment of accuracy of adaptive integration of cut cells for laminar fluid-structure interaction problems
Get PDFFinite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are cut by the interface between two different domains need to be integrated using special techniques in order to obtain optimal convergence rates and accurate fluxes across the interface. The adaptive integration technique in which the cells are recursively subdivided is one of the popular techniques for the numerical integration of cut-cells due to its advantages over tessellation, particularly for problems involving complex geometries in three dimensions. Although adaptive integration does not impose any limitations on the representation of the geometry of immersed solids as it requires only point location algorithms, it becomes computationally expensive for recovering optimal convergence rates. This paper presents a comprehensive assessment of the adaptive integration of cut-cells for applications in computational fluid dynamics and fluid-structure interaction. We assess the effect of the accuracy of integration of cut cells on convergence rates in velocity and pressure fields, and then on forces and displacements for fluid-structure interaction problems by studying several examples in two and three dimensions. By taking the computational cost and the accuracy of forces and displacements into account, we demonstrate that numerical results of acceptable accuracy for FSI problems involving laminar flows can be obtained with only fewer levels of refinement. In particular, we show that three levels of adaptive refinement are sufficient for obtaining force and displacement values of acceptable accuracy for laminar fluid-structure interaction problems
A new family of projection schemes for the incompressible NavierâStokes equations with control of high-frequency damping
Get PDFA simple spatially discrete model problem consisting of mass points and dash-pots is presented which allows for the assessment of the properties of different projection schemes for the solution of the incompressible NavierâStokes equations. In particular, the temporal accuracy, the stability and the numerical damping are investigated. The present study suggests that it is not possible to formulate a second order accurate projection/pressure-correction scheme which possesses any high-frequency damping. Motivated by this observation two new families of projection schemes are proposed which are developed from the generalised midpoint rule and from the generalised-α method, respectively, and offer control over high-frequency damping. Both schemes are investigated in detail on the basis of the model problem and subsequently implemented in the context of a finite element formulation for the incompressible NavierâStokes equations. Comprehensive numerical studies of the flow in a lid-driven cavity and the flow around a cylinder are presented. The observations made are in agreement with the conclusions drawn from the model problem
A numerical framework for the simulation of coupled electromechanical growth
Get PDFElectro-mechanical response exists in growing materials such as biological tissues and hydrogels, influencing the growth process, pattern formation and geometry remodelling. To gain a better understanding of the mechanism of the coupled effects of growth and electric fields on the deformation behaviour, a finite element framework for coupled electro-elastic growth is established. Based on the extended volume growth theory, the governing equations of the growing electro-elastic solid are obtained. A coupled three-field mixed displacement-pressure-potential finite element formulation using infâsup stable combinations is adapted. The finite element formulation is implemented in ABAQUS via a user element subroutine. The implementation is validated first by comparing the deformation and stress components of a growing tubular structure under axial strain and radial voltage. Using the example of a bi-layer beam actuator, it is illustrated that growth parameters and the external voltage can precisely control the bending angle. The framework is then applied to simulate pattern formation and transition behaviour, such as doubling and tripling of wrinkles, by specifying growth parameters and external voltage in a 3D stiff film/soft substrate structure. Furthermore, the suppression of wrinkles by applying external voltage is demonstrated. It is observed that the electric field plays a significant role in stress redistribution and guiding growth, resulting in the promotion or suppression of wrinkles, which is demonstrated by the numerical simulation of a long tubular structure. The proposed finite element scheme provides an accurate, efficient and stable tool for numerical simulation of electro-elastic solids incorporating growth effect, which can be used for understanding coupled growth phenomenon in biological soft matter and developing smart devices for medical treatment
New iterative and staggered solution schemes for incompressible fluidâstructure interaction based on DirichletâNeumann coupling
Get PDFIn the presence of strong added mass effects, partitioned solution strategies for incompressible fluid-structure interaction are known to lack robustness and computational efficiency. A number of strategies have been proposed to address this challenge. However, these strategies are often complicated or restricted to certain problem classes and generally require intrusive modifications of existing software. In this work, the well-known Dirichlet-Neumann coupling is revisited and a new combined two-field relaxation strategy is proposed. A family of efficient staggered schemes based crucially on a force predictor is formulated alongside the classical iterative approach. Both methodologies are rigorously analyzed on the basis of a linear model problem derived from a simplified fluid-conveying elastic tube. The investigation suggests that both the robustness and the efficiency of a partitioned Dirichlet-Neumann coupling scheme can be improved by a relatively small nonintrusive modification of a standard implementation. The relevance of the model problem analysis for finite element-based computational fluid-structure interaction is demonstrated in detail for a submerged cylinder subject to an external force
Effect of pulsating flow on flow-induced vibrations of circular and square cylinders in the laminar regime
Get PDFThrough fluid-structure interaction simulations, this study assesses the dynamic response characteristics of elastically mounted circular and square cylinders subjected to pulsating inflow conditions, providing valuable insights into the analysis and optimization of these systems. The main focus of the present work is on analyzing the effects of two factors: (i) the ratio of the oscillatory velocity component to the steady velocity component in pulsating flow (flow ratio) and (ii) the ratio of the oscillation frequency of pulsating flow to the natural frequency of the structure (frequency ratio). The simulation results for different parameters of interest are analysed using Fourier analysis and Poincaré maps of time series data, and contour plots of vorticity. For the circular cylinder, it is found that cylinder loses synchronization in lock-in as the flow and frequency ratios are increased. Three distinct vibration patterns of vortex-induced vibration are observed for selected combinations of flow and frequency ratios at a Reynolds number of 110 for circular cylinder. For the galloping of square cylinder at a Reynolds number of 250, it is found that the instability and nonlinearity of vortex shedding become more pronounced as the flow ratio increases
