Stress Mode Superposition for a Priori Detection of Highly ‎Stressed Areas: Mode Normalisation and Loading Influence

Document Type : Research Paper


Technical University Berlin, Institute of Mechanics, TU-Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany‎


From the economic and technical point of view, the reduction of development periods and required resources represent a considerable benefit. For the reduction of numerical effort and processed data in numerical stress analysis, the present paper is focused onto the investigation of an efficient method for the a priori detection of a structural component’s highly stressed areas. Based on the theory of stress mode superposition and the frequency domain solution of the decoupled equations of motion, an analytically consistent approach for a priori mode superposition is presented. In this context, the influence of multiaxial loading and mode normalisation is investigated. Validation is performed on a simplified industrial model of a twist-beam rear axle.


Main Subjects

[1] Marinkovic, D., Zehn, M., Survey of finite element method-based real-time simulations, Applied Sciences, 9(14), 2019, 2775.
[2] Marinkovic, D., Zehn, M., Pavlovic, A., Highly efficient FE simulations by means of simplified corotational formulation, Operational Research in Engineering Sciences: Theory and Applications, 3(2), 2020, 74-86.
[3] Mastrogiannakis, I., Vosniakos, G.-C., Exploring structural design of the Francis hydro-turbine blades using composite materials, Facta Universitatis-Series Mechanical Engineering, 18(1), 2020, 43-55.
[4] Ahmadifar, A., Zamani, M.R., Davar, A., Jam, J.E., Beni, M. H., Experimental and numerical buckling analysis of carbon fiber composite lattice conical structure before and after lateral impact, Journal of Applied and Computational Mechanics, 6(4), 2020, 813-822.
[5] Fallahi, N., Viglietti, A., Carrera, E., Pagani, A., Zappino, E., Effect of fiber orientation path on the buckling, free vibration and static analyses of variable angle tow panels, Facta Universitatis-Series Mechanical Engineering, 18(2), 2020, 165-188.
[6] Rama, G., Marinkovic, D., Zehn, M., High performance 3-node shell element for linear and geometrically nonlinear analysis of composite laminates, Composites Part B: Engineering, 151, 2018, 118-126.
[7] Marinković, D., Rama, G., Zehn, M., Abaqus implementation of a corotational piezoelectric 3-node shell element with drilling degree of freedom, Facta Universitatis-Series Mechanical Engineering, 17(2), 2019, 269-283.
[8] Rama, G., Marinković, D., Zehn, M., Efficient three-node finite shell element for linear and geometrically nonlinear analyses of piezoelectric laminated structures, Journal of Intelligent Material Systems and Structures, 29(3), 2018, 345-357.
[9] Pavlovic, A., Fragassa, C., Geometry optimization by FEM simulation of the automatic changing gear, Reports in Mechanical Engineering, 1(1), 2020, 199-205.
[10] Ye, Y., Zhu, W., Jiang, J., Xu, Q., Ke, Y., Design and optimization of composite sub-stiffened panels, Composite Structures, 240, 2020, 112084.
[11] Miao, B.R., Luo, Y.X., Peng, Q.M., Qiu, Y.Z., Chen, H., Yang, Z.K., Multidisciplinary design optimization of lightweight carbody for fatigue assessment, Materials & Design, 194, 2020, 108910.
[12] Minak, G., Brugo, T., Fragassa, C., Pavlovic, A., Zavatta, N., De Camargo, V. F., Structural Design and Manufacturing of a Cruiser Class Solar Vehicle, Journal of Visualized Experiments, 143, 2019, e58525.
[13] Paz, M., Structural dynamics: theory and computation, Springer Science & Business Media, 2012.
[14] Marinković, D., Zehn, M., Consideration of stress stiffening and material reorientation in modal space based finite element solutions, Physical Mesomechanics, 21(4), 2018, 341-350.
[15] Pavlovic, A., Sintoni, D., Minak, G., Fragassa, C., On the Modal Behaviour of Ultralight Composite Sandwich Automotive Panels, Composite Structures, 248, 2020, 112523.
[16] Fragassa, C., Pavlovic, A., Minak, G., On the Structural Behaviour of a CFRP Safety Cage in a Solar Powered Electric Vehicle, Composite Structures, 252, 2020, 112698.
[17] Pavlovic, A., Fragassa, C., Investigating the resistance of concrete reinforced walls to high velocity projectiles, Engineering Structures, 174, 2018, 384–395.
[18] Craig, R., Kurdila, A., Fundamentals of Structural Dynamics. 2nd ed., John Wiley & Sons, New Jersey, 2006.
[19] Huang, L., Agrawal, H., Kurudiyara, P., Dynamic Durability Analysis of Automotive Structures, SAE Transactions, 1998, 474-480.
[20] Brincker, R., Ventura, C., Introduction to Operational Modal Analysis, John Wiley & Sons, Chichester, 2015.
[21] Lopez-Aenlle, M., Brincker, R., Fernandez, P., Fernandez-Canteli, A., On exact and approximated formulations for scaling mode shapes in operational modal analysis by mass and stiffness change, Journal of Sound and Vibration, 331(3), 2012, 622–637.
[22] Bernal, D., A receptance based formulation for modal scaling using mass perturbations, Mechanical Systems and Signal Processing, 25(2), 2011, 621–629.
[23] Brownjohn, J.M.W., Pavic, A., Experimental methods for estimating modal mass in footbridges using human-induced dynamic excitation, Engineering Structures, 29(11), 2007, 2833–2843.
[24] Yam, L.Y., Leung, T.P., Li, D.B., Xue, K.Z., Theoretical and experimental study of modal strain analysis, Journal of Sound and Vibration, 191(2), 1996, 251-260.
[25] Lu, G.Y., Zheng, D., Venkatakrishnaiah, S., Vest, T., A Dynamic Durability Analysis Method and Application to a Battery Support Subsystem, SAE Technical Paper, 2004, No. 2004-01-0874.
[26] Vellaichamy, S., Keshtkar, H., New approaches to modal transient fatigue analysis, SAE Transactions, 2000, 845-850.
[27] Mršnik, M., Slavič, J., Boltežar, M., Vibration fatigue using modal decomposition, Mechanical Systems and Signal Processing, 98, 2018, 548-556.
[28] Braccesi, C., Cianetti, F., Tomassini, L., An innovative modal approach for frequency domain stress recovery and fatigue damage evaluation, International Journal of Fatigue, 91, 2016, 382-396.
[29] Lu, Y., Xiang, P., Dong, P., Zhang, X., Zeng, J., Analysis of the effects of vibration modes on fatigue damage in high-speed train bogie frames, Engineering Failure Analysis, 89, 2018, 222-241.
[30] Albuquerque, C., Silva, A.L., de Jesus, A.M., Calçada, R., An efficient methodology for fatigue damage assessment of bridge details using modal superposition of stress intensity factors, International Journal of Fatigue, 81, 2015, 61-77.
[31] Gu, Z., Mi, C., Wang, Y., Jiang, J., A-type frame fatigue life estimation of a mining dump truck based on modal stress recovery method, Engineering Failure Analysis, 26, 2012, 89-99.
[32] Horas, C.S., Correia, J.A.F.O., De Jesus, A.M.P., Calçada, R., Aenlle, M.L., Kripakaran, P., Fernandez-Canteli, A., Application of modal superposition technique in the fatigue analysis using local approaches, Procedia Engineering, 160, 2016, 45-5.
[33] Tran, V.X., Geniaut, S., Galenne, E., Nistor, I., A modal analysis for computation of stress intensity factors under dynamic loading conditions at low frequency using extended finite element method, Engineering Fracture Mechanics, 98, 2013, 122-136.
[34] Huang, L., Agrawal, H., Borowski, V., Durability analysis of a vehicle body structure using modal transient methods, Proceedings of the 15th International Modal Analysis Conference, Orlando, Florida, 407-414, 1997.
[35] Lesiuk, G., Smolnicki, M., Mech, R., Ziety, A., Fragassa, C., Analysis of fatigue crack growth under mixed mode (I + II) loading conditions in rail steel using CTS specimen, Engineering Failure Analysis, 109, 2020, 104354.
[36] Huang, L., Agrawal, H., US Patent No. 6212486, 2001.
[37] Lin, R.M., Mottershead, J.E., Ng, T.Y., A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives, Mechanical Systems and Signal Processing, 138, 2020, 106536.
[38] Tigh Kuchak, A.J., Marinkovic, D., Zehn, M., Finite element model updating - Case study of a rail damper, Structural Engineering and Mechanics, 73(1), 2020, 27-35.
[39] Fotouhi, S., Akrami, R., Ferreira-Green, K., Naser, G., Fotouhi, M., Fragassa, C., Piezoelectric PVDF sensor as a reliable device for strain/load monitoring of engineering structures, IOP Conference Series: Materials Science and Engineering, 659(1), 2019, 012085.
[40] Fragassa, C., Minak, G., Pavlovic, A. Measuring Deformations in a Telescopic Boom under Static and Dynamic Load Conditions, Facta Universitatis-Series Mechanical Engineering, 18(2), 2020, 315–328.
[41] Pavlovic, A., Sintoni, D., Fragassa, C., Minak, G., Multi-Objective Design Optimization of the Reinforced Composite Roof in a Solar Vehicle, Applied Sciences, 10, 2020, 2665.
[42] Veltri, M., FEM Techniques for High Stress Detection in Accelerated Fatigue Simulation, Journal of Physics: Conference Series, 744, 2016, 012137.
[43] Zhou, Y., Wu, S., Trisovic, N., Fei, Q., Tan, Z., Modal Strain Based Method for Dynamic Design of Plate-Like Structures, Shock and Vibration, 2016, 2016, 2050627.
[44] Zhou, Y., Fei, Q., Wu, S., Utilization of modal stress approach in random-vibration fatigue evaluation, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 231(14), 2017, 2603–2615.
[45] Zhou, Y., Tao, J., Theoretical and numerical investigation of stress mode shapes in multi-axial random fatigue, Mechanical Systems and Signal Processing, 127, 2019, 499–512.
[46] Strzalka, C., Zehn, M., The influence of loading position in a priori high stress detection using mode superposition, Reports in Mechanical Engineering, 1(1), 2020, 93-102.
[47] Clough, R.W., Penzien, J., Dynamics of Structures, McGraw‐Hill, New York, 1975.
[48] Aenlle, M., Juul, M., Brincker, R., Modal Mass and Length of Mode Shapes in Structural Dynamics, Shock and Vibration, 2020, 2020, 8648769.