A computationally efficient numerical model for a dynamic analysis of thin plates based on the combined finite–discrete element method

Abstract This paper presents a new numerical model for a static and dynamic analysis of thin plate structures based on the combined finite–discrete element method (FDEM). The model uses three-noded triangular finite elements taking into account linear-elastic material behaviour, finite rotations, finite displacements and small strains. The model is implemented into the open source FDEM package ‘Yfdem’. Performance of the new numerical model was demonstrated on simple benchmark tests by a comparison with known analytical and numerical results.

[1]  J-P Latham,et al.  Some computational and algorithmic developments in computational mechanics of discontinua , 2004, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[2]  Antonio Munjiza,et al.  An M(M−1K)m proportional damping in explicit integration of dynamic structural systems , 1998 .

[3]  Laurent Daudeville,et al.  Multidomain finite and discrete elements method for impact analysis of a concrete structure , 2009 .

[4]  M. H. Aliabadi,et al.  A boundary element method for dynamic plate bending problems , 2000 .

[5]  Hae-Soo Oh,et al.  Meshfree particle methods for thin plates , 2012 .

[6]  Phill-Seung Lee,et al.  The MITC3+ shell element in geometric nonlinear analysis , 2015 .

[7]  E. Ventsel,et al.  Thin Plates and Shells: Theory: Analysis, and Applications , 2001 .

[8]  E. Ramm,et al.  A unified approach for shear-locking-free triangular and rectangular shell finite elements , 2000 .

[9]  R. M. Natal Jorge,et al.  Analysis of thick plates by the natural radial element method , 2013 .

[10]  A. Munjiza.  The Combined Finite-Discrete Element Method , 2004 .

[11]  A. Munjiza,et al.  Large Strain Finite Element Method: A Practical Course , 2015 .

[12]  Robert L. Taylor,et al.  Triangular finite elements with rotational degrees of freedom and enhanced strain modes , 2000 .

[13]  H. W. Lee,et al.  Natural element approximation of Reissner–Mindlin plate for locking-free numerical analysis of plate-like thin elastic structures , 2013 .

[14]  N. W. M. John,et al.  The combined finite–discrete element method for structural failure and collapse , 2004 .

[15]  Bernardin Peroš,et al.  MULTIPLICATIVE DECOMPOSITION BASED FDEM MODEL FOR MEMBRANE STRUCTURES , 2014 .

[16]  Željana Nikolić,et al.  A combined finite-discrete element analysis of dry stone masonry structures , 2013 .

[17]  Eugenio Oñate,et al.  Rotation-free triangular plate and shell elements , 2000 .

[18]  Julian A. T. Dow,et al.  A Unified Approach to the Finite Element Method and Error Analysis Procedures , 1998 .

[19]  R. M. Natal Jorge,et al.  A natural neighbour meshless method with a 3D shell-like approach in the dynamic analysis of thin 3D structures , 2011 .

[20]  D. Chapelle,et al.  The Finite Element Analysis of Shells - Fundamentals , 2003 .

[21]  A. Munjiza,et al.  Fracture and fragmentation of thin shells using the combined finite–discrete element method , 2013 .

[22]  T. Vo-Duy,et al.  Static and free vibration analyses of stiffened folded plates using a cell-based smoothed discrete shear gap method (CS-FEM-DSG3) , 2015, Appl. Math. Comput..

[23]  Byung Chai Lee,et al.  Development of a strain-smoothed three-node triangular flat shell element with drilling degrees of freedom , 2014 .

[24]  E. Albuquerque,et al.  Transient dynamic analysis of shear deformable shallow shells using the boundary element method , 2015 .

[25]  Esteban Rougier,et al.  Computational Mechanics of Discontinua , 2011 .

[26]  R. M. Natal Jorge,et al.  Composite laminated plate analysis using the natural radial element method , 2013 .

[27]  Kyung K. Choi,et al.  Meshfree analysis and design sensitivity analysis for shell structures , 2002 .

[28]  R. Clough,et al.  Dynamics Of Structures , 1975 .