2,753 research outputs found
Survey of Finite Element Method-Based Real-Time Simulations
The finite element method (FEM) has deservedly gained the reputation of the most powerful, highly efficient, and versatile numerical method in the field of structural analysis. Though typical application of FE programs implies the so-called āoff-lineā computations, the rapid pace of hardware development over the past couple of decades was the major impetus for numerous researchers to consider the possibility of real-time simulation based on FE models. Limitations of available hardware components in various phases of developments demanded remarkable innovativeness in the quest for suitable solutions to the challenge. Different approaches have been proposed depending on the demands of the specific field of application. Though it is still a relatively young field of work in global terms, an immense amount of work has already been done calling for a representative survey. This paper aims to provide such a survey, which of course cannot be exhaustive
KE-formulacija za aplikacije virtualne stvarnosti
Virtual reality (VR), as a novel technology, represents one of the most powerful tools to assist or even play the major role in many areas, such as development of new designs, training medical practitioners or assembly operators, entertaining industry, etc. On the other hand, the finite element method (FEM) imposed itself as an essential technical support for the needs of computing flexible bodiesā deformational behavior. FEM together with CAD are important ingredients of VR. In the VR applications that imply interactive simulations with flexible bodies included, the efficiency of FEM formulations is of crucial importance. The paper presents a co-rotational FEM-formulation developed to meet the needs of simulating geometrically nonlinear deformational behavior at interactive frame rates. It is presented here in combination with a rather simple linear tetrahedral element. The formulation is enriched with a coupled-mesh technique to enable the usage of rougher FEM models to compute deformational behavior of complex geometries. The advantages of an iterative solver and the solution procedure for both static and dynamic analyses are discussed.Virtualna stvarnost (VR), kao nova tehnologija, predstavlja jednu od najmoÄnijih alatki koje podržavaju rad ili Äak igraju glavnu ulogu u mnogim podruÄjima, kao Å”to su razvoj novih dizajna, trening lijeÄnika ili montažera, industrija zabave, itd. S druge strane, metoda konaÄnih elemenata (MKE) se nametnula kao osnovna tehniÄka podrÅ”ka za potrebe proraÄunavanja deformacijskog ponaÅ”anja elastiÄnih tijela. MKE je zajedno s CAD-om, važan dio VR-a. U VR aplikacijama koje podrazumijevaju interaktivnu simulaciju s elastiÄnim tijelima, efikasnost MKE formulacije je od presudne važnosti. Rad predstavlja korotacijsku MKE formulaciju razvijenu s ciljem simuliranja geometrijski nelinearnog ponaÅ”anja u interaktivnoj domeni. Formulacija je predstavljena u kombinaciji s vrlo jednostavnim linearnim elementom tipa tetraedra. Formulacija je proÅ”irena tehnikom spregnutih mreža kako bi se omoguÄilo koriÅ”tenje grubljih MKE modela za odreÄivanje deformacijskog ponaÅ”anja složenih geometrija. Razmotrene su prednosti iterativnog solvera kao i procedura rjeÅ”avanja statiÄke i dinamiÄke analize
On large deformations of thin elasto-plastic shells: Implementation of a finite rotation model for quadrilateral shell element
A large-deformation model for thin shells composed of elasto-plastic material is presented in this work, Formulation of the shell model, equivalent to the two-dimensional Cosserat continuum, is developed from the three-dimensional continuum by employing standard assumptions on the distribution of the displacement held in the shell body, A model for thin shells is obtained by an approximation of terms describing the shell geometry. Finite rotations of the director field are described by a rotation vector formulation. An elasto-plastic constitutive model is developed based on the von Mises yield criterion and isotropic hardening. In this work, attention is restricted to problems where strains remain small allowing for all aspects of material identification and associated computational treatment, developed for small-strain elastoplastic models, to be transferred easily to the present elasto-plastic thin-shell model. A finite element formulation is based on the four-noded isoparametric element. A particular attention is devoted to the consistent linearization of the shell kinematics and elasto-plastic material model, in order to achieve quadratic rate of asymptotic convergence typical for the Newton-Raphson-based solution procedures. To illustrate the main objective of the present approach-namely the simulation of failures of thin elastoplastic shells typically associated with buckling-type instabilities and/or bending-dominated shell problems resulting in formation of plastic hinges-several numerical examples are presented, Numerical results are compared with the available experimental results and representative numerical simulations
On the relation between different parametrizations of finite rotations for shells
In this work we present interrelations between different finite rotation parametrizations for geometrically exact classical shell models (i.e. models without drilling rotation). In these kind of models the finite rotations are unrestricted in size but constrained in the 3-d space. In the finite element approximation we use interpolation that restricts the treatment of rotations to the finite element nodes. Mutual relationships between different parametrizations are very clearly established and presented by informative commutative diagrams. The pluses and minuses of different parametrizations are discussed and the finite rotation terms arising in the linearization are given in their explicit forms
A comparison of Finite Elements for Nonlinear Beams: The absolute nodal coordinate and geometrically exact formulations
Two of the most popular finite element formulations for solving nonlinear beams are the absolute nodal coordinate and the geometrically exact approaches. Both can be applied to problems with very large deformations and strains, but they differ substantially at the continuous and the discrete levels. In addition, implementation and run-time computational costs also vary significantly. In the current work, we summarize the main features of the two formulations, highlighting their differences and similarities, and perform numerical benchmarks to assess their accuracy and robustness. The article concludes with recommendations for the choice of one formulation over the other
Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity
A recent unsymmetric 4ānode, 8āDOF plane finite element USāATFQ4 is generalized to hyperelastic finite deformation analysis. Since the trial functions of USāATFQ4 contain the homogenous closed analytical solutions of governing equations for linear elasticity, the key of the proposed strategy is how to deal with these linear analytical trial functions (ATFs) during the hyperelastic finite deformation analysis. Assuming that the ATFs can properly work in each increment, an algorithm for updating the deformation gradient interpolated by ATFs is designed. Furthermore, the update of the corresponding ATFs referred to current configuration is discussed with regard to the hyperelastic material model, and a specified model, neoāHookean model, is employed to verify the present formulation of USāATFQ4 for hyperelastic finite deformation analysis. Various examples show that the present formulation not only remain the high accuracy and mesh distortion tolerance in the geometrically nonlinear problems, but also possess excellent performance in the compressible or quasiāincompressible hyperelastic finite deformation problems where the strain is large
Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling
The computational homogenization of hyperelastic solids in the geometrically
nonlinear context has yet to be treated with sufficient efficiency in order to
allow for real-world applications in true multiscale settings. This problem is
addressed by a problem-specific surrogate model founded on a reduced basis
approximation of the deformation gradient on the microscale. The setup phase is
based upon a snapshot POD on deformation gradient fluctuations, in contrast to
the widespread displacement-based approach. In order to reduce the
computational offline costs, the space of relevant macroscopic stretch tensors
is sampled efficiently by employing the Hencky strain. Numerical results show
speed-up factors in the order of 5-100 and significantly improved robustness
while retaining good accuracy. An open-source demonstrator tool with 50 lines
of code emphasizes the simplicity and efficiency of the method.Comment: 28 page
Stress resultant plasticity for shells revisited
In this work, we revisit the stress resultant elastoplastic geometrically exact shell finite element formulation that is based on the IlyushināShapiro two-surface yield function with isotropic and kinematic hardening. The main focus is on implicit projection algorithms for computation of updated values of internal variables for stress resultant shell elastoplasticity. Four different algorithms are derived and compared. Three of them yield practically identical final results, yet they differ considerably in computational efficiency and implementation complexity, since they solve different sets of equations and they use different procedures that choose active yield surfaces. One algorithm does not provide acceptable accuracy. It turns out that the most simple and straightforward algorithm performs surprisingly well and efficiently. Several numerical examples are presented to illustrate the IlyushināShapiro stress resultant shell formulation and the numerical performance of the presented integration algorithms
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