Accurate numerical modeling of multifield piezoelectric materials is challenging because of the inherent electro-mechanical coupling effect and material anisotropic behaviors. The modeling becomes ...even more difficult especially for problems with non-smooth solutions like crack under dynamic loading. We present in this paper an extension of the extended isogeometric analysis (XIGA) for simulation of two-dimensional fracture mechanics problems in piezoelectric materials under dynamic and static coupled electromechanical loads. The discretization of problem domain is based on basis functions generated from NURBS, which are used for both geometric description and approximation of solution field variables. To capture the discontinuity across the crack-faces and the singularity at the crack-tip, the isogeometric approximation is locally enriched by discontinuous Heaviside function and asymptotic crack-tip branch functions. The sixfold enrichment functions particularly suitable for electromechanical crack-tip singularity of piezoelectric materials are used. To evaluate the generalized fracture parameters, a domain-form of electromechanical interaction integral is employed. For dynamic analysis, the implicit time integration scheme considering inertial effect is taken. Five numerical examples for single and mixed-modes of impermeable cracks are considered and the generalized fracture parameters under dynamic and static loads are analyzed. The accuracy and effectiveness of the proposed XIGA are illustrated through numerical investigations of the generalized dynamic and static fracture parameters. Numerical results are validated against the reference solutions derived from the boundary element methods. The effects of some numerical aspect ratios on generalized fracture parameters are also investigated. Additionally, we present some numerical results of quasi-static crack propagation in piezoelectric solids using the developed XIGA, taking fracture toughness anisotropy of polarized electroelastic materials into account, and employing the maximum modified hoop stress intensity factor criterion for predicting the growing direction of crack.
•XIGA dynamic and static fracture formulation in piezoelectricity is developed.•Crack growth modeling in brittle piezoelectric solids is presented.•Static generalized intensity factors of cracked piezoelectric solids are analyzed.•Transient dynamic responses of impermeable and permeable cracks are studied.•Effects of polarization, enrichments, meshes, loadings, etc. on GIFs are investigated.
An effective, simple, robust and locking-free plate formulation is proposed to analyze the static bending, buckling, and free vibration of homogeneous and functionally graded plates. The simple ...first-order shear deformation theory (S-FSDT), which was recently presented in Thai and Choi (2013) 11, is naturally free from shear-locking and captures the physics of the shear-deformation effect present in the original FSDT, whilst also being less computationally expensive due to having fewer unknowns. The S-FSDT requires C1-continuity that is simple to satisfy with the inherent high-order continuity of the non-uniform rational B-spline (NURBS) basis functions, which we use in the framework of isogeometric analysis (IGA). Numerical examples are solved and the results are compared with reference solutions to confirm the accuracy of the proposed method. Furthermore, the effects of boundary conditions, gradient index, and geometric shape on the mechanical response of functionally graded plates are investigated.
Isogeometric simulation of acoustic radiation Mederos, Victoria Hernández; Hernández, Eduardo Moreno; Sarlabous, Jorge Estrada ...
Mathematics and computers in simulation,
9/2023
Journal Article
Recenzirano
Odprti dostop
In this paper we discuss the numerical solution of the Helmholtz equation with mixed boundary conditions on a 2D physical domain Ω. The so called radiation problem depends on the constant wavenumber ...k, that in some medical applications can be of order of thousands. For these values of k the classical Finite Element Method (FEM) faces up several numerical difficulties. To mitigate these limitations we apply the Isogeometric Analysis (IgA) to compute the approximated solution uh. Main steps of IgA are discussed and specific proposals for their fulfillment are addressed, with focus on some aspects not covered in available publications. In particular, we introduce a low distortion quadratic NURBS parametrization of Ω that represents exactly its boundary and contributes to the accuracy of uh. Our approach is non-isoparametric since uh is a bicubic tensor product polynomial B-spline function on Ω. This allows to improve the numerical solution refining the approximation space and keeping the coarser parametrization of the domain. Moreover, we discuss the role of the number of degrees of freedom in the directions perpendicular and longitudinal to wave front and its relationship with the noise and the shift in amplitude and phase of uh. The linear system derived from IgA discretization of the radiation problem is solved using GMRES and we show though experiments that the incomplete factorization of the Complex Shifted Laplacian provides a very good preconditioner. To solve the radiation problem, we have implemented IgA approach using the open source package GeoPDEs. A comparison with FEM is included, to provide evidence that IgA approach is superior since it is able to reduce significantly the pollution error, especially for high values of k, producing additionally smoother solutions which depend on less degrees of freedom.
We present and analyze a new stable space–time Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The ...discrete bilinear form is elliptic on the IgA space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the IgA spaces yields an a priori discretization error estimate with respect to the discrete norm. The theoretical results are confirmed by several numerical experiments with low- and high-order IgA spaces.
Abstract This paper presents a parameterisation framework based on (inverted) elliptic PDEs for addressing the planar parameterisation problem of finding a valid description of the domain’s interior ...given no more than a spline-based description of its boundary contours. The framework is geared towards isogeometric analysis (IGA) applications wherein the physical domain is comprised of more than four sides, hence requiring more than one patch. We adopt the concept of harmonic maps and propose several PDE-based problem formulations capable of finding a valid map between a convex parametric multipatch domain and the piecewise-smooth physical domain with an equal number of sides. In line with the isoparametric paradigm of IGA, we treat the parameterisation problem using techniques that are characteristic for the analysis step. As such, this study proposes several IGA-based numerical algorithms for the problem’s governing equations that can be effortlessly integrated into a well-developed IGA software suite. We augment the framework with mechanisms that enable controlling the parametric properties of the outcome. Parametric control is accomplished by, among other techniques, the introduction of a curvilinear coordinate system in the convex parametric domain, for which more general elliptic PDEs are adopted. Depending on the application, parametric control allows for building desired features into the computed map, such as homogeneous cell sizes or boundary layers.
Wet grinding is a process that involves many different subprocesses. In order to model this highly complex process, efficient models of the individual subprocesses are required that are robust enough ...to be used in multiphysics analyses. To approach the modelling of the macroscopic hydrodynamic effects of the grinding wheel as one component of the analysis, this paper is dedicated to the thermo-hydrodynamic problem and its modelling by expanding the isogeometric analysis (IGA) from hydrodynamic analysis to the thermal consideration. Extended by a consideration of flow effects in areas with high surface gradients and particular attention paid to the necessary stabilization of the governing equations, thermo-hydrodynamic systems with temperature- and pressure-dependent fluid properties are considered. Selected benchmarks feasible for computational fluid dynamics (CFD) simulations are used to demonstrate the good suitability of this modelling strategy. The presented modelling strategies can also be applied to lubricated technical systems in general, beyond wet grinding systems.
The study using numerical methods on porous functionally graded (FG) nanoplates is still somewhat limited. This paper focuses on porosity-dependent nonlinear transient analysis of FG nanoplates using ...isogeometric finite element approach. In order to capture the small size effects, the Eringen's nonlocal elasticity based on higher order shear deformation theory (HSDT) are used to model the porous FG nanoplates. Two distributions of porosities inside FG materials are incorporated and defined via a modified rule of mixture. The nonlinear transient nonlocal governing equations under transverse dynamic loads are formulated by using the von Kármán strains and are solved by Newmark time integration scheme to obtain geometrically nonlinear responses. It is indicated that nonlinear transient deflections of the porous FG nanoplate are significantly influenced by material composition, porosity, nonlocal parameters, volume fraction exponent, porosity distributions, geometrical parameters and dynamic load characteristics.
•Vibration of porous plates with porosity distributions along the thickness and the in-plane directions.•Application of IGA for solving free vibration problems of porous plates.•Some new results for ...porous plates are presented.•The effects of porosity coefficient, boundary conditions and geometric parameters are investigated.
The main purpose of this paper is to study the free vibration of porous square plate, circular plate, and rectangle plate with a central circular hole in the framework of isogeometric analysis (IGA). Generally, the porosity distributions of plates are assumed to happen in the thickness direction. However, the graded distributions of porosity may occur through the in-plane direction of plates. Therefore, porosity distributions along both the thickness direction and in-plane direction are considered in this study. The displacement fields are described by the first order shear deformation theory (FSDT) and the exact geometric models are formulated wholly by non-uniform rational B-spline (NURBS) basis functions, which bear high-order continuity inherently. To ensure the versatility of IGA-FSDT, several numerical examples for isotropic and porous plates with different boundary conditions and various types of porosity distributions are presented. Moreover, some innovative results are presented and discussed, which can be the benchmark data for other algorithm researches. The effects of porosity coefficient, boundary conditions and geometric parameters on the free vibration of porous plates are investigated comprehensively.
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This paper presents a novel method for topology optimization of vibrating structures interacted with acoustic wave for the purpose of minimizing radiated sound power level. We consider exterior ...acoustic fields and bi-material shell models without damping in this work. Within the isogeometric analysis framework, we employ Catmull–Clark subdivision surfaces to construct geometries and discretize physical fields. The isogeometric finite element method with Kirchhoff–Love shell elements is coupled with the isogeometric boundary element method in acoustics. The topology optimization is performed through density-based approaches, in which the sensitivities are evaluated with adjoint variable methods. Numerical experiments demonstrate the validity and effectiveness of the algorithm for topology optimization of structural-acoustic interaction systems.
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