Application of the mode-shape expansion based on model order reduction methods to a composite structure

The application of different mode-shape expansion (MSE) methods to a CFRP based on model order reduction (MOR) and component mode synthesis (CMS) methods is evaluated combining the updated stiffness parameters of the full FE model obtained with a mix-numerical experimental technique (MNET) in a previous work. The eigenvectors and eigenfrequencies of the different MSE methods obtained are compared with respect to the experimental measurements and with a full FE model solutions using the modal assurance criteria (MAC). Furthermore, the stiffness and mass weighted coefficients (K-MAC and M-MAC respectively) are calculated and compared to observe the influence of the different subspace based expansion methods applying the MAC criteria. The K-MAC and M-MAC are basically the MAC coefficients weighted by a partition of the global stiffness and mass matrices respectively. The best K-MAC and M-MAC results per paired mode-sensor are observed in the subspace based expansion MODAL/SEREP and MDRE-WE methods using the updated stiffness parameters. A strong influence of the subspace based on MOR using MSE methods is observed in the K-MAC and M-MAC criteria implemented in SDTools evaluating the stiffness parameters in a contrieved example

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

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

Modellreduktion bei Verbundwerkstoffkomponenten und -baugruppen als Teil komplexer technischer Systeme zur Simulation des dynamischen Gesamtverhaltens

The composite components and model order reduction (MOR) methods are widely used to improve the weight/strength ratio and the computational time respectively in different areas of the industry. The objective of this research is to evaluate the dynamic behaviour applying a MOR method in a composite component assembly. A new mixed numerical-experimental technique (MNET) is developed to obtain accurate stiffness parameters in a composite component and then the Craig-Bampton model order reduction (CBMOR) method is applied in terms of a substructure/super element technique using the automatic multi-layer substructuring (AMLS) method. The MNET consists of a correlation between a composite component assembly using experimental measurements and a 2D finite element (FE) model using an equivalent single layer (ESL) homogenized laminate theory including transverse shear effects (discrete Mindlin Kirchhoff triangle (DMKT)). Curve-fitting algorithms are used to improve the accuracy of the correlation. The correlation is performed based on the modal assurance criterion (MAC) and the updating is calculated with a design of experiments (DOE). A DOE is a regression analysis used to obtain a simple mathematical model (transfer function/surface response) to update the stiffness parameters. The dynamic behaviour consists of the application of a CBMOR and AMLS methods to the FE model in the previous part. Different modal assurance criteria were applied to correlate experimental measurements versus the dynamic behaviour response of the FE models. For comparative purposes the stiffness parameters obtained in MATLAB-SDTools with the new MNET were used in MSC/NASTRAN, ABAQUS, and few mode shape expansion techniques respectively to validate the results. Based on the results, it can be concluded that the stiffness parameters obtained with the new MNET were fundamental for the validation, updating and accuracy applying the CBMOR and AMLS methods in a composite component.Komponenten aus Verbundwerkstoffen und Methoden zur Modellreduktion finden breite Anwendung in verschiedenen Bereichen der Industrie, um das Verhältnis zwischen Gewicht und Festigkeit zu verbessern beziehungsweise die Berechnungszeit zu verkürzen. Ziel der vorliegenden Arbeit ist die Auswertung des dynamischen Verhaltens einer Verbundwerkstoffkomponente unter Anwendung eines Modellreduktionsverfahrens. Eine neue gemischte numerisch-experimentelle Methode zur Ermittlung akkurater Steifigkeitsparameter sowie der Einsatz des Craig-Bampton-Verfahrens in Form einer Substruktur-/Superelement-Technik unter Verwendung der automatischen Multi-Layer-Substruktur-Methode. Der gemischte numerisch-experimentele Methode besteht aus einem Zusammenhang zwischen experimentellen Messungen an einer Baugruppe aus Verbundwerkstoffkomponenten und einem 2D-Finite-Elemente-Modell unter Anwendung einer homogenisierten äquivalenten Single-Layer-Laminattheorie einschließlich transversaler Schereffekte (diskretes Mindlin-Kirchhoff-Dreieck). Mithilfe von Kurvenanpassungsalgorithmen wird die Genauigkeit der Korrelation erhöht. Die Korrelation erfolgt auf der Grundlage des MAC-Kriteriums (Modal Assurance Criterion) und die Modelloptimierung wird durch eine Versuchsplanung ermittelt, eine Regressionsanalyse zur Erlangung eines einfachen mathematischen Modells (Übertragungsfunktion/ Systemantwort der Oberfläche) für die Aktualisierung der Steifigkeitsparameter. Der dynamischen Verhaltens besteht aus der Anwendung des Craig-Bampton-Verfahrens und der automatischen Multi-Layer-Substruktur-Methode auf das existierende FE-Modell. Für die Anpassung des dynamischen Verhaltens des FE-Modells an die experimentellen Messungen werden verschiedene COMAC-Kriterien (Coordinate Modal Assurance Criteria) benutzt. Zu Vergleichszwecken und zur Validierung der Ergebnisse werden die mit der neuen Methode in MATLAB-SDTools erhaltenen Steifigkeitsparameter in MSC/NASTRAN, ABAQUS beziehungsweise mit weiteren Schwingungsformausbreitungstechniken verwendet. Auf Grundlage der Ergebnisse lässt sich folgern, dass die mit der neuen Methode ermittelten Parameter von wesentlicher Bedeutung für die Validierung, Optimierung und Genauigkeit bei der Anwendung des Craig-Bampton-Verfahrens und der automatischen Multi-Layer-Substruktur-Methode auf eine Verbundwerkstoffkomponente sind