A Modification on Applied Element Method for Linear Analysis of Structures in the Range of Small and Large Deformations Based on Energy Concept

Document Type : Research Papers


Babol Noshirvani University of Technology


In this paper, the formulation of a modified applied element method for linear analysis of structures in the range of small and large deformations is expressed. To calculate deformations in the structure, the minimum total potential energy principle is used. This method estimates the linear behavior of the structure in the range of small and large deformations, with a very good accuracy and low analytical time. The results show that analysis of a console beam by proposed method, even with minimum numbers of elements, in range of small deformations, has a computation error of less than 2%. Meanwhile, solving the same problem by Applied Element Method (AEM), has more than 31% error. Also, the buckling and post-buckling behavior of the structure, within the range of large deformations, is well-suited. So, with minimum number of elements, and very high accuracy, the buckling behavior of the fixed-base column was simulated. Also, the computational time of the proposed method is less than 40 percent of the computational time in the application of the applied elements method with 10 series of connection springs.


Alizadeh Behjani, M.R., Gaffari Motlagh, Y., Bayly, A. and Hassanpour, A. (2019). "Assessment of blending performance of parametrical powder mixtures in a continuous mixer using Discrete Element Method (DEM)", Powder Technology, 319, 313-322.
Bićanić, N. (2017). Discrete Element methods, Part 1: Solids and structures, https://doi.org/10.1002/9781119176817.ecm2006.
Borja, H. and Thomas, V. (2015), "Energy-based method for sudden column failure scenarios: theoretical, numerical and experimental analysis", Safety, Robustness and Condition Assessment of Structures, IABSE Workshop, Helsinki.
Gohel, V., Patel, P.V. and Joshi, D. (2013). "Analysis of frame using Applied Element Method (AEM)", Procedia Engineering, 51, 176-183.
Govender, N., Wilke, D. and Kok, S. (2016). "Blaze-DEMGPU: Modular high performance DEM framework for the GPU architecture", SoftwarX, 5, 62-66.
Kawai, T. (1980). "Some consideration on the finite element method", Numerical Methods in Engineering, 16, 81-120.
Liu, M. and Piemoz, A. (2016). "Energy-based pulldown analysis for assessing the progressive collapse potential of steel frame buildings", Engineering Structures, 123, 372-378.
Lupoae, M. and Constantin, D. (2013). "Theoretical and experimental research on progressive collapse of RC frame buildings", Urbanism, Architecture, Constructions, 4(3), 71-87.
Meguro, K. and Hakuno, M. (1989) "Fracture analysis of structures by the modified distinct element method", Structural Engineering / Earthquake Engineeing, 6(2), 283s-294s.
Meguro, K. and Tagel-Din, H. (1997). "A new efficient technique for fracture analysis of structures", Bulletin of Earthquake Resistant Structure Research, University of Tokyo, 30, 103-116.
Munjiza, A., Owen, D.R.J. and Bicanic, N. (1995). "Combined Finite-Discrete Element method in transient dynamics of fracturing soils", International Journal of Engineering Computation, 12, 145-174.
Prionas, I. (2016). "Progressive collapse analysis of existing buildings, A performance based approach", 16th Conference on Earthquake Engineering (16WCEE), Santiago, Chile.
Shakeri, A. and Bargi, Kh. (2015). "Use of applied element method for structural Analysis", KSCE Journal of Civil Engineering, 19(5), 1375-1384.
Shi, G.H. (1992). "Discontinuous deformation analysis: A new numerical model for the statics and dynamics of deformable block structures", Engineering Computations, 9(2), 157-168.
Simon, A. and Dragomir, C.S. (2013). "The simulation of an industrial building demolition", Urbanism, Architecture, Constructions, 4(2), 2069-6469
Soltani, M. and Moshirabadi, S. (2019). "Implementation of smeared crack approach in rigid block and spring modeling of reinforced concrete", Engineering Structures, 201, 109779.
Szabo J. Gaspar Z. and Tarnai, T. (1986). Post-buckling of elastic structures, Elsevier Science Publishing Co. Inc., Budapest.
Tagel-Din, H. (1998). "A new efficient method for nonlinear, large deformation and collapse analysis of structures", PhD Thesis, Civil Engineering Department, University of Tokyo.
Tavakoli H.R. and Akbarpoor, S. (2014). “Effect of brick infill panel on the seismic safety of reinforced concrete frames under progressive collapse”, Computers and Concrete, 13(6), 749-764.
Tavakoli H.R. and Kiakojouri, F. (2013). “Numerical study of progressive collapse in framed structures: A new approach for dynamic column removal”, International Journal of Engineering, Transaction A: Basics, 26(7), 685-692.
Timoshenko, S.P and Gere, J.M. (1961). Theory of elastic stability, McGraw-Hill Publication, 07-Y85821-7.
Ueda, M. and Kambayaashi, A. (1993) "Size effect analysis using RBSM with Vornori elements", International Workshop on Size Effect in Concrete Structures, Japan Concrete Institute (JCI), 199-210.
Williams, G.N., Pande, G. and Beer, J.R. (1990). Numerical methods in rock mechanics, Chichester: Wiley.
Williams, J.R, Hocking, G. and Mustoe, G.G.W. (1985). "The theoretical basis of the discrete element method", In Proceedings of NUMETA’85 (Numerical Methods of Engineering, Theory and Applications), Rotterdam: A.A. Balkema, 897-906.
Worakanchana, K. and Meguro, K. (2008). "Voroni applied element method for structural analysis: Theory and application for linear and non-linear materials", The 14th World Conference on Earthquake Engineering, Beijing, China.
Zhang, L.W., Ademiloye, A.S. and Liew, K.M. (2019). "Meshfree and particle methods in biomechanics: Prospects and challenges", Archives of Computational Methods in Engineering, 26(5), 1547-1576.