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 “off-line” 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

Application of the Craig-Bampton model order reduction method to a composite structure: MACco, COMAC, COMAC-S and eCOMAC

The Craig-Bampton model order reduction (CBMOR) method based on the Rayleigh-Ritz approach was applied in a previous work to simulate dynamic behavior of a composite structure (CFRP) using the modal assurance criteria (MAC) and cross orthogonality (XOR) to validate the correlation. Different coordinate modal assurance criteria are applied to complement and verify the eigenfrequencies and eigenvectors obtained of the full and reduced models using substructures (super-elements). An improvement is observed per paired mode-sensor with the MAC per coordinates criterion (MACco) in a CFRP once the stiffness parameters are updated in the full model applying a mix-numerical experimental technique (MNET) using a design of experiments (DOE). The coordinate modal assurance criteria (COMAC) and the scaleCOMAC (COMACS) results of the full models display the best results respect to the reduced model. Furthermore, slight improvement of the enhanced COMAC (eCOMAC) results are observed in the reduced model despite having lower MAC performance. This approach complements the results of the previous work using several COMAC techniques, and demostrates the feasibility to achieve low COMACs results in the reduced finite element model once the stiffness parameters of the full element model are updated. The example was prepared and solved with MSC/NASTRAN SOL103 and SDTools-MATLAB for comparative purposes

Nachnutzbare FEM-Software in der DDR

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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 bodies’ 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 najmoćnijih alatki koje podržavaju rad ili čak igraju glavnu ulogu u mnogim područjima, kao što su razvoj novih dizajna, trening liječnika ili montažera, industrija zabave, itd. S druge strane, metoda konačnih elemenata (MKE) se nametnula kao osnovna tehnička podrška za potrebe proračunavanja deformacijskog ponašanja elastičnih tijela. MKE je zajedno s CAD-om, važan dio VR-a. U VR aplikacijama koje podrazumijevaju interaktivnu simulaciju s elastičnim tijelima, efikasnost MKE formulacije je od presudne važnosti. Rad predstavlja korotacijsku MKE formulaciju razvijenu s ciljem simuliranja geometrijski nelinearnog ponašanja u interaktivnoj domeni. Formulacija je predstavljena u kombinaciji s vrlo jednostavnim linearnim elementom tipa tetraedra. Formulacija je proširena tehnikom spregnutih mreža kako bi se omogućilo korištenje grubljih MKE modela za određivanje deformacijskog ponašanja složenih geometrija. Razmotrene su prednosti iterativnog solvera kao i procedura rješavanja statičke i dinamičke analize

THE ANALYSIS OF FEM RESULTS CONVERGENCE IN MODELLING PIEZOELECTRIC ACTIVE SHELL STRUCTURES

The field of active/adaptive structures has been the subject of intense interest over the past couple of decades. The progress in this research field strongly depends on the availability of adequate and reliable modelling tools. Regarding structural analysis in general, the finite element method (FEM) has imposed itself as the method of choice for modelling and simulation. Piezoelectric active structures are characterized by strong enough coupling between the mechanical field and the electric field, which is further used for the realization of active structural behaviour. The descriptions of the mechanical and electrical field as well as their coupling significantly affect the convergence of the FEM results with mesh refinement, which may proceed in a trend different to what is commonly expected when FEM is applied to purely mechanical problems. The paper considers this aspect by using two quadratic shell type finite elements developed for modelling piezoelectric composite laminates. Both full and uniformly reduced integration techniques are taken into consideration in a set of examples involving composite laminates with active piezoelectric layers

THE ANALYSIS OF FEM RESULTS CONVERGENCE IN MODELLING PIEZOELECTRIC ACTIVE SHELL STRUCTURES

The field of active/adaptive structures has been the subject of intense interest over the past couple of decades. The progress in this research field strongly depends on the availability of adequate and reliable modelling tools. Regarding structural analysis in general, the finite element method (FEM) has imposed itself as the method of choice for modelling and simulation. Piezoelectric active structures are characterized by strong enough coupling between the mechanical field and the electric field, which is further used for the realization of active structural behaviour. The descriptions of the mechanical and electrical field as well as their coupling significantly affect the convergence of the FEM results with mesh refinement, which may proceed in a trend different to what is commonly expected when FEM is applied to purely mechanical problems. The paper considers this aspect by using two quadratic shell type finite elements developed for modelling piezoelectric composite laminates. Both full and uniformly reduced integration techniques are taken into consideration in a set of examples involving composite laminates with active piezoelectric layers

MODAL TRIGGERED NONLINEARITIES FOR DAMAGE LOCALIZATION IN THIN WALLED FRC STRUCTURES – A NUMERICAL STUDY

This paper presents a novel method for detecting locations of damages in thin walled structural components made of fiber reinforced composites (FRC). Therefore, the change of harmonic distortion, which is found by current research to be very sensitive to delamination, under resonant excitation will be derived from FEM-simulation. Based on the linear modal description of the undamaged structure and the damage-induced nonlinearities represented by a nonlinear measure, two spatial damage indexes have been formulated.The main advantage of this novel approach is that the information about the defect is represented mainly by changes in the modal harmonic distortion (MHD), which just needs to be measured in one (or few) structural points. The spatial resolution is given by the pairwise coupling of the MHD with the corresponding mode shapes

APPLICATION OF THE CRAIG-BAMPTON MODEL ORDER REDUCTION METHOD TO A COMPOSITE STRUCTURE: MAC AND XOR

The Craig-Bampton model order reduction (CBMOR) method based on the Rayleigh-Ritz approach is applied to dynamic behavior simulation of a composite structure in order to verify the method’s feasibility and accuracy. The principle of this method is to represent a coupled component model based on the mass, damping and stiffness matrices. The methodology consists of a finite element model based on the classical laminate theory (CLT), a design of experiment to improve the modal assurance criteria (MAC) and experimental results in order to validate the reduced model based on CBMOR method and substructures (super-elements). Experimental modal analysis has been performed using a scanner laser Doppler vibrometer (SLDV) in order to assess the quality of the finite element models. The MAC and cross orthogonality MAC (XOR) values are computed to verify the eigenfrequencies and eigenvectors. This approach demonstrates the feasibility of using CBMOR for composite structures. The example is prepared and solved with MSC/NASTRAN SOL103. The design of experiments (DOE) method has been applied in order to identify the critical parameters and thus obtain high MAC values

High performance 3-node shell element for linear and geometrically nonlinear analysis of composite laminates

Thin-walled structures hold primacy among modern engineering structures. All the advantages offered by the curved geometry and thinness of the walls come even more to the fore when combined with exquisite properties of fiber-reinforced composite laminates. Directionally dependant material properties open vast possibilities for tailoring global structural properties and, therewith, optimization. Successful design of such structures calls for high performance shell type finite elements. This paper presents a linear triangular shell element based on the equivalent single-layer approach and the first-order shear deformation theory. The shear locking effect is resolved by the descrete shear gap (DSG) approach combined with the cell smoothing technique. To improve the element performance with respect to the membrane behavior, the assumed natural deviatoric strains (ANDES) formulation is applied, with necessary modifications to meet the requirements of curved structures with anisotropic material properties. Geometric nonlinearities are addressed by the co-rotational formulation. Examples demonstrate the element applicability and performance

Efficient three-node finite shell element for linear and geometrically nonlinear analyses of piezoelectric laminated structures

Fiber-reinforced composite laminates involving piezoelectric layers represent a very attractive material system. It combines the advantages of using rather lightweight and stiff material with the possibility of sensing structural changes and actively influencing its state by means of sensors and actuators. A three-node shell element is proposed as an efficient tool for modeling structures made of such a material system. Thoroughly tested solutions are implemented to resolve locking problems intrinsic for shell elements. The embedded piezoelectric layers are considered to be polarized in the thickness direction. Furthermore, the extension of the formulation to geometrically nonlinear finite element analysis is based on a co-rotational formulation. Numerical examples are given to demonstrate the applicability of developed element in linear and geometrically nonlinear finite element analyses covering both actuator and sensor cases