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Search results for: ISOGEOMETRIC ANALYSIS, KIRCHHOFF–LOVE SHELLS, MULTIPLICATIVE SPLIT, NONLINEAR FINITE ELEMENT METHODS, SURFACE ELASTICITY, VISCOELASTICITY
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An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split
PublicationThis work presents a numerical formulation to model isotropic viscoelastic material behavior for membranes and thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system,which allows the representation of general surfaces and deformations. The kinematics follow from Kirchhoff–Love theory and the discretization makes use of isogeometric shape functions. A multiplicative split of the surface...
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Nonlinear material identification of heterogeneous isogeometric Kirchhoff–Love shells
PublicationThis work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous materialdistributions based on an efficient isogeometric shell formulation. It uses nonlinear hyperelastic material models suitable fordescribing incompressible material behavior as well as initially curved shells. The material distribution is discretized by bilinearelements such that the nodal values...
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A new anisotropic bending model for nonlinear shells: Comparison with existing models and isogeometric finite element implementation
PublicationA new nonlinear hyperelastic bending model for shells formulated directly in surface form is presented, and compared to four existing prominent bending models. Through an essential set of elementary nonlinear bending test cases, the membrane and bending stresses of each model are examined analytically. Only the proposed bending model passes all the test cases, while the other bending models either fail or only pass the test cases for...
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A simple and efficient hybrid discretization approach to alleviate membrane locking in isogeometric thin shells
PublicationThis work presents a new hybrid discretization approach to alleviate membrane locking in isogeometric finite element formulations for Kirchhoff–Love shells. The approach is simple, and requires no additional dofs and no static condensation. It does not increase the bandwidth of the tangent matrix and is effective for both linear and nonlinear problems. It combines isogeometric surface discretizations with classical Lagrange-based...
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A general isogeometric finite element formulation for rotation‐free shells with in‐plane bending of embedded fibers
PublicationThis article presents a general, nonlinear isogeometric finite element formulation for rotation-free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting, and bending - both in-plane and out-of-plane. These capabilities allow for the simulation of large sheets of heterogeneous and fibrous materials either with or without matrix, such as textiles, composites, and pantographic structures. The work...
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Isogeometric Shell FE Analysis of the Human Abdominal Wall
PublicationIn this paper a nonlinear isogeometric Kirchhoff-Love shell model of the human abdominal wall is proposed. Its geometry is based on in vivo measurements obtained from a polygon mesh that is transformed into a NURBS surface, and then used directly for the finite element analysis. The passive response of the abdominal wall model under uniform pressure is considered. A hyperelastic membrane model based on the Gasser-Ogden-Holzapfel...
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Material Identification of the Human Abdominal Wall Based On the Isogeometric Shell Model
PublicationThe human abdominal wall is an object of interest to the research community in the context of ventral hernia repair. Computer models require a priori knowledge of constitutive parameters in order to establish its mechanical response. In this work, the Finite Element Model Updating (FEMU) method is used to identify an heterogeneous shear modulus distribution for a human abdominal wall model, which is based on nonlinear isogeometric...
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Galerkin formulations of isogeometric shell analysis: Alleviating locking with Greville quadratures and higher-order elements
PublicationWe propose new quadrature schemes that asymptotically require only four in-plane points for Reissner–Mindlin shell elements and nine in-plane points for Kirchhoff–Love shell elements in B-spline and NURBS-based isogeometric shell analysis, independent of the polynomial degree p of the elements. The quadrature points are Greville abscissae associated with pth-order B-spline basis functions whose continuities depend on the specific...
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A general theory for anisotropic Kirchhoff–Love shells with in-plane bending of embedded fibers
PublicationThis work presents a generalized Kirchhoff–Love shell theory that can explicitly capture fiber-induced anisotropy not only in stretching and out-of-plane bending, but also in in-plane bending. This setup is particularly suitable for heterogeneous and fibrous materials such as textiles, biomaterials, composites and pantographic structures. The presented theory is a direct extension of classical Kirchhoff–Love shell theory to incorporate...
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An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors
PublicationAn isogeometric finite element formulation for geometrically and materially nonlinear Timoshenko beams is presented, which incorporates in-plane deformation of the cross-section described by two extensible director vectors. Since those directors belong to the space R3, a configuration can be additively updated. The developed formulation allows direct application of nonlinear three-dimensional constitutive equations without zero...
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Surface finite viscoelasticity and surface anti-plane waves
PublicationWe introduce the surface viscoelasticity under finite deformations. The theory is straightforward generalization of the Gurtin–Murdoch model to materials with fading memory. Surface viscoelasticity may reflect some surface related creep/stress relaxation phenomena observed at small scales. Discussed model could also describe thin inelastic coatings or thin interfacial layers. The constitutive equations for surface stresses are...
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An isogeometric finite element formulation for frictionless contact of Cosserat rods with unconstrained directors
PublicationThis paper presents an isogeometric finite element formulation for nonlinear beams with impenetrability constraints, based on the kinematics of Cosserat rods with unconstrained directors. The beam cross-sectional deformation is represented by director vectors of an arbitrary order. For the frictionless lateral beam-to-beam contact, a surface-to-surface contact algorithm combined with an active set strategy and a penalty method...
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Geometrically nonlinear analysis of shells - Benchmark problems for Autocad Robot Analysis Professional
PublicationThe aim of this work is to verify the suitability of commercial engineering software for geometrically nonlinear analysis of shells. This paper deals with the static, geometrically nonlinear analysis of shells made of an isotropic material. The Finite Element Method (FEM) is chosen to solve the problem. The results of the commercial software Autocad Robot Structural Analysis Professional (ARSAP) are compared with the litera-ture...
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Geometrically nonlinear finite element simulation of smart piezolaminated plates and shells
PublicationW pracy zaproponowano powłokowy element skończony pozwalający na uwzględnienie efektu piezoelektrycznego. Element został wykorzystany w podejściu Lagrange'a, które wymaga starannego dobrania definicji wielkości mechanicznych i elektrycznych. Zależności przemieszczenie-odkształcenie zbudowano na bazie teorii małych odkształceń i umiarkowanych obrotów. Założono liniowy rozkład pól odkształceń i pola elektrycznego po grubości powłoki....
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2-D constitutive equations for orthotropic Cosserat type laminated shells in finite element analysis
PublicationWe propose 2-D Cosserat type orthotropic constitutive equations for laminated shells for the purpose of initial failure estimation in a laminate layer. We use nonlinear 6-parameter shell theory with asymmetric membrane strain measures and Cosserat kinematics as the framework. This theory is specially dedicated to the analysis of irregular shells, inter alia, with orthogonal intersections, since it takes into account the drilling...
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Finite element modeling of plastic hinges based on ductility demand-capacity method using nonlinear material for dynamic analysis
PublicationThe article discusses modeling plastic hinges in reinforced concrete interme-diate supports using finite elements methods. The ductility demand-capacitymethod was used to determine the geometrical parameters of cross-section plas-ticization zones, their ability to move and rotate, as well as their ductility. Dueto the varied geometry and stiffness of the supports and their nonlinear behav-ior under dynamic load, this method was...
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On the Bending of Multilayered Plates Considering Surface Viscoelasticity
PublicationWe discuss the bending resistance of multilayered plates taking into account surface/interfacial viscoelasticity. Within the linear surface viscoelasticity we introduce the surface/interfacial stresses linearly dependent on the history of surface strains. In order to underline the surface viscoelasticity contribution to the bending response we restrict ourselves to the elastic behaviour in the bulk. Using the correspondence principle...
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Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches
PublicationThis paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite...
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Fractional Spectral and Fractional Finite Element Methods: A Comprehensive Review and Future Prospects
PublicationIn this article, we will discuss the applications of the Spectral element method (SEM) and Finite element Method (FEM) for fractional calculusThe so-called fractional Spectral element method (f-SEM) and fractional Finite element method (f-FEM) are crucial in various branches of science and play a significant role. In this review, we discuss the advantages and adaptability of FEM and SEM, which provide the simulations of fractional...
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Four-node semi-EAS element in six-field nonlineartheory of shells
PublicationW pracy sformułowano 4-węzłowy powłokowy element skończony dla konstrukcji powłokowych. Element opracowano w ramach nieliniowej 6-parametrowej teorii powłok z niesymetrycznymi miarami odkształceń membranowych. Kinematyka powłoki jest opisana przez dwa pola: translacji i obrotów, przy czym wszystkie trzy parametry obrotu traktowane są jako niezależne. W wyniku tego sformułowany element nadaje się do analizy struktur powłokowych...
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Geometrically nonlinear FEM analysis of FGM shells based on neutral physical surface approach in 6-parameter shell theory
PublicationThe paper presents the formulation of the elastic constitutive law for functionally graded materials (FGM) on the grounds of nonlinear 6-parameter shell theory with the 6th parameter being the drilling degree of freedom. The material law is derived by through-the-thickness integration of the Cosserat plane stress equations. The constitutive equations are formulated with respect to the neutral physical surface. The influence of...
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Nonlinear FEM analysis of irregular shells composed of fiber metal laminates
PublicationThe paper deals with the analysis of failure initiation in shells made of Fiber Metal Laminates (FML). The elas-tic material law for orthotropic lamina is stated accounting for asymmetric in-plane stress and strain measures. The asymmetry results from the employed general nonlinear 6-field shell theory where the generalized dis-placements involve the translation and the proper rotation field. The novelty of the presented results...
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A selectively reduced degree basis for efficient mixed nonlinear isogeometric beam formulations with extensible directors
PublicationThe effect of higher order continuity in the solution field by using NURBS basis function in isogeometric analysis (IGA) is investigated for an efficient mixed finite element formulation for elastostatic beams. It is based on the Hu–Washizu variational principle considering geometrical and material nonlinearities. Here we present a reduced degree of basis functions for the additional fields of the stress resultants and strains...
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On nonlinear dilatational strain gradient elasticity
PublicationWe call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the...
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Galerkin formulations with Greville quadrature rules for isogeometric shell analysis: Higher order elements and locking
PublicationWe propose new Greville quadrature schemes that asymptotically require only four in-plane points for Reissner-Mindlin (RM) shell elements and nine in-plane points for Kirchhoff-Love (KL) shell elements in B-spline and NURBS-based isogeometric shell analysis, independent of the polynomial degree of the elements. For polynomial degrees 5 and 6, the approach delivers high accuracy, low computational cost, and alleviates membrane and...
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Dynamic fracture of brittle shells in a space-time adaptive isogeometric phase field framework
PublicationPhase field models for fracture prediction gained popularity as the formulation does not require the specification of ad-hoc criteria and no discontinuities are inserted in the body. This work focuses on dynamic crack evolution of brittle shell structures considering large deformations. The energy contributions from in-plane and out-of-plane deformations are separately split into tensile and compressive components and the resulting...
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Macromodeling techniques for accelerated finite element analysis
PublicationThis paper deals with the Model Order Reduction applied locally in the Finite Element Method (FEM) analysis. Due to the reduction process, blocks of FEM system matrices associated with selected subregions of the computational domain are projected onto the subspaces spanned by the vectors of suited orthogonal projection basis. In effect, large and sparse FEM matrices are replaced with small and dense ones, called macromodels. This...
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Elastoplastic nonlinear FEM analysis of FGM shells of Cosserat type
PublicationThe paper is a continuation of [1] where the formulation of the elastic constitutive law for functionally graded materials (FGM) on the grounds of nonlinear 6-parameter shell theory with the 6th parameter (the drilling degree of freedom) was presented. Here the formulation is extended to the elasto-plastic range. The material law is based on Cosserat plasticity and employs the well-known Tamura-Tomota-Ozawa (TTO) [2] mixture...
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Reduced-order models in the finite element analysis
PublicationA novel technique of incorporating macromodels into finite element electromagnetic analysis of waveguide components is presented. Macromodels are generated by using a model order reduction algorithm (ENOR), which results in significant decrease of the number of variables, that describe the computational region. Proposed technique allows for using a few independent macromodels as well as to duplicating one macromodel in many subregions...
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A higher order transversely deformable shell-type spectral finite element for dynamic analysis of isotropic structures
PublicationThis paper deals with certain aspects related to the dynamic behaviour of isotropic shell-like structures analysed by the use of a higher order transversely deformable shell-type spectral finite element newly formulated and the approach known as the Time-domain Spectral Finite Element Method (TD-SFEM). Although recently this spectral approach is reported in the literature as a very powerful numerical tool used to solve various...
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Geometrically nonlinear analysis of shells
PublicationArtykuł porusza zagadnienia nieliniowej analizy powłok wykonanych z materiałów izotropowych. Obliczenia wykonano przy wykorzystaniu dwóch komercyjnych programów wykorzystujących Metodę Elementów Skończonych (Robot Millennium v. 19.0 i MSC.Marc v.2005r2 ). Główną uwagę skupiono na zjawisku zakleszczenia.
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An optimal form of the finite element mass matrix in the analysis of longitudinal vibrations of rods
PublicationIn this paper, an attempt is made to find the optimal form of the mass matrix of a rod finite element, which allows one to obtain the smallest errors in the longitudinal frequency determination of natural vibrations of any boundary conditions within the whole range of determined frequencies. It is assumed that the mass matrix can be treated as a linear combination of the consistent and diagonal matrices. Based on analytical considerations,...
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Geometrically Nonlinear Analysis of Functionally Graded Shells Based on 2-D Cosserat Constitutive Model
PublicationIn this paper geometrically nonlinear analysis of functionally graded shells in 6-parameter shell theory is presented. It is assumed that the shell consists of two constituents: ceramic and metal. The mechanical properties are graded through the thickness and are described by power law distribution. Formulation based on 2-D Cosserat constitutive model is used to derive constitutive relation for functionally graded shells. Numerical...
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Strongly anisotropic surface elasticity and antiplane surface waves
PublicationWithin the new model of surface elasticity, the propagation of anti-plane surface waves is discussed. For the proposed model, the surface strain energy depends on surface stretching and on changing of curvature along a preferred direction. From the continuum mechanics point of view, the model describes finite deformations of an elastic solid with an elastic membrane attached on its boundary reinforced by a family of aligned elastic...
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A Review: Applications of the Spectral Finite Element Method
PublicationThe Spectral Finite Element Technique (SFEM) has Several Applications in the Sciences, Engineering, and Mathematics, which will be Covered in this Review Article. The Spectral Finite Element Method (SFEM) is a Variant of the Traditional Finite Element Method FEM that Makes use of Higher Order Basis Functions (FEM). One of the most Fundamental Numerical Techniques Employed in the Numerical Simulation is the SFEM, which Outperforms...
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Analysis of Corrugated Coaxial Line with the Use of Body of Revolution and Finite Element Method
PublicationA combination of the body-of-revolution and finite element methods is utilized to the analysis of coaxial lines with corrugated rod and wall. Both periodic and non-periodic structures can be investigated. As the structure is axially symmetrical the two dimensional scalar-vector finite element method can be used, which allows for the investigation of complex geometries and is computationally efficient. A generalized impedance matrix...
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Harmonic Vibrations of Nanosized Magnetoelectric Bodies with Coupled Surface and Interphase Effects: Mathematical Models and Finite Element Approaches
PublicationThe harmonic problems for piezomagnetoelectric nanosized bodies with taking into account the coupled damping and surface effects are considered on the base of the generalized Gurtin-Murdoch model. In the development of previous investigations, the coupled mechanical, electric and magnetic surface effects with surface inertial terms are introduced into the model. For a homogeneous model, the composite material is considered as homogeneous...
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Nonlocal Vibration of Carbon/Boron-Nitride Nano-hetero-structure in Thermal and Magnetic Fields by means of Nonlinear Finite Element Method
PublicationHybrid nanotubes composed of carbon and boron-nitride nanotubes have manifested as innovative building blocks to exploit the exceptional features of both structures simultaneously. On the other hand, by mixing with other types of materials, the fabrication of relatively large nanotubes would be feasible in the case of macroscale applications. In the current article, a nonlinear finite element formulation is employed to deal with...
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Efficient and robust quadratures for isogeometric analysis: Reduced Gauss and Gauss–Greville rules
PublicationThis work proposes two efficient quadrature rules, reduced Gauss quadrature and Gauss–Greville quadrature, for isogeometric analysis. The rules are constructed to exactly integrate one-dimensional B-spline basis functions of degree p, and continuity class C^{p−k}, where k is the highest order of derivatives appearing in the Galerkin formulation of the problem under consideration. This is the same idea we utilized in Zou et al....
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An algorithm for enhancing macromodeling in finite element analysis of waveguide components
PublicationAn algorithm for enhancing the finite element method with local model order reduction is presented. The proposed technique can be used in fast frequency domain simulation of waveguide components and resonators. The local reduction process applied to cylindrical subregions is preceded by compression of the number of variables on its boundary. As a result,the finite element large system is converted into a very compact set of linear...
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Finite element modelling of a historic church structure in the context of a masonry damage analysis
PublicationThe paper includes a case study of modelling a real historic church using the finite element method (FEM) based on laser scans of its geometry. The main goal of the study was the analysis of the causes of cracking and crushing of masonry walls. An FEM model of the structure has been defined in ABAQUS. A non-linear dynamic explicit analysis with material model including damage plasticity has been performed. A homogenization procedure...
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Efficient Finite Element Analysis of Axially Symmetrical Waveguides and Waveguide Discontinuities
PublicationA combination of the body-of-revolution and finite element methods is adopted for full-wave analysis of waveguides and waveguide discontinuities involving angular field variation. Such an approach is highly efficient and much more flexible than analytical techniques. The method is performed in two different cases: utilizing a generalized impedance matrix to determine the scattering parameters of a single waveguide section and utilizing...
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Large deformation finite element analysis of undrained pile installation
PublicationIn this paper, a numerical undrained analysis of pile jacking into the subsoil using Abaqus software suit has been presented. Two different approaches, including traditional Finite Element Method (FEM) and Arbitrary Lagrangian–Eulerian (ALE) formulation, were tested. In the first method, the soil was modelled as a two-phase medium and effective stress analysis was performed. In the second one (ALE), a single-phase medium was assumed...
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Singular Surface Curves in the Resultant Thermodynamics of Shells
PublicationWithin six-parameter shells theory we discuss the governing equations of shells with material or non-material singular curves. By singular curve we mean a surface curve where are discontinuities in some surface fields. As an example we consider shells with junctions and shells undergoing stress-induced phase transitions.
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Nonlinear resultant theory of shells accounting for thermodiffusion
PublicationThe complete nonlinear resultant 2D model of shell thermodiffusion is developed. All 2D balance laws and the entropy imbalance are formulated by direct through-the-thickness integration of respective 3D laws of continuum thermodiffusion. This leads to a more rich thermodynamic structure of our 2D model with several additional 2D fields not present in the 3D parent model. Constitutive equations of elastic thermodiffusive shells...
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Comparison of modal and finite-element methods in the vibrational analysis of marine propulsion systems
PublicationW okrętowych układach napędowych występują dwa typy części składowych. Pierwszym z nich są odcinki wałów, które należą do elementów o ciągłym rozkładzie własności masowych, sprężystych i tłumiących oraz elementy o parametrach skupionych, do których można zaliczyć śrubę napędową, tarcze sprzęgieł i inne. W pracy porównano dwie metody modelowania takich układów. Pierwsza z nich związana jest z tworzeniem modeli przybliżonych w oparciu...
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Macromodels for Efficient Analysis of Open-Region Problems Using the Finite Element Method
PublicationThis paper presents a local model-order reduction, called macromodeling, applied to speed-up the simulations of open-region problems, analyzed by means of finite element method. This technique is illustrated by a numerical example, which deals with a dielectric resonator antenna (DRA). The obtained results show that the proposed approach is reliable and can significantly increase the standard finite element method efficiency.
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GPU-Accelerated 3D Mesh Deformation for Optimization Based on the Finite Element Method
PublicationThis paper discusses a strategy for speeding up the mesh deformation process in the design-byoptimization of high-frequency components involving electromagnetic field simulations using the 3D finite element method (FEM). The mesh deformation is assumed to be described by a linear elasticity model of a rigid body; therefore, each time the shape of the device is changed, an auxiliary elasticity finite-element problem must be solved....
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Reliable Greedy Multipoint Model-Order Reduction Techniques for Finite-Element Analysis
PublicationA new greedy multipoint model-order reduction algorithm for fast frequency-domain finite-element method simulations of electromagnetic problems is proposed. The location of the expansion points and the size of the projection basis are determined based on a rigorous error estimator. Compared to previous multipoint methods, the quality of the error estimator is significantly improved by ensuring the orthogonality of the projection...
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Strong ellipticity conditions and infinitesimal stability within nonlinear strain gradient elasticity
PublicationWe discuss connections between the strong ellipticity condition and the infinitesimal instability within the nonlinear strain gradient elasticity. The strong ellipticity (SE) condition describes the property of equations of statics whereas the infinitesimal stability is introduced as the positive definiteness of the second variation of an energy functional. Here we establish few implications which simplify the further analysis...