The strong formulation finite element method: stability and accuracy

The Strong Formulation Finite Element Method (SFEM) is a numerical solution technique for solving arbitrarily shaped structural systems. This method uses a hybrid scheme given by the Differential Quadrature Method (DQM) and the Finite Element Method (FEM). The SFEM takes the best from DQM and FEM giving a highly accurate strong formulation based technique with the adaptability of finite elements. The present study investigates the stability and accuracy of SFEM when applied to 1D and 2D structural components, such as rods, beams, membranes and plates using analytical and semi-analytical well-known solutions. The numerical results show that the present approach can be very accurate using a small number of grid points and elements, when it is compared to standard FEM.

[1]  Erasmo Viola,et al.  Analytical and numerical results for vibration analysis of multi-stepped and multi-damaged circular arches , 2007 .

[2]  E. Viola,et al.  On Static Analysis of Composite Plane State Structures viaGDQFEM and Cell Method , 2013 .

[3]  Chuei-Tin Chang,et al.  New insights in solving distributed system equations by the quadrature method—II. Numerical experiments , 1989 .

[4]  D. Gottlieb,et al.  Numerical analysis of spectral methods , 1977 .

[5]  E. Viola,et al.  Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories , 2013 .

[6]  C. Bert,et al.  Differential Quadrature Method in Computational Mechanics: A Review , 1996 .

[7]  Erasmo Viola,et al.  Vibration Analysis of Damaged Circular Arches with Varying Cross-section , 2005 .

[8]  Chang Shu,et al.  Numerical computation of three-dimensional incompressible viscous flows in the primitive variable form by local multiquadric differential quadrature method , 2006 .

[9]  R. Bellman,et al.  DIFFERENTIAL QUADRATURE AND LONG-TERM INTEGRATION , 1971 .

[10]  Nicholas Fantuzzi,et al.  Mechanics of Laminated Composite Doubly-Curved Shell Structures. The Generalized Differential Quadrature Method and the Strong Formulation Finite Element Method , 2014 .

[11]  J. N. Reddy,et al.  Winkler–Pasternak foundation effect on the static and dynamic analyses of laminated doubly-curved and degenerate shells and panels , 2014, Composites Part B: Engineering.

[12]  Nicholas Fantuzzi,et al.  Generalized Differential Quadrature Finite Element Method for vibration analysis of arbitrarily shaped membranes , 2014 .

[13]  J. Reddy.  Mechanics of laminated composite plates : theory and analysis , 1997 .

[14]  Chuei-Tin Chang,et al.  New insights in solving distributed system equations by the quadrature method—I. Analysis , 1989 .

[15]  Alfred G. Striz,et al.  Static analysis of structures by the quadrature element method , 1994 .

[16]  Thomas J. R. Hughes,et al.  Isogeometric Analysis: Toward Integration of CAD and FEA , 2009 .

[17]  Alfredo Liverani,et al.  Laminated composite rectangular and annular plates: A GDQ solution for static analysis with a posteriori shear and normal stress recovery , 2012 .

[18]  Elena Ferretti,et al.  Soft Core Plane State Structures Under Static Loads UsingGDQFEM and Cell Method , 2013 .

[19]  Nicholas Fantuzzi,et al.  Radial basis function method applied to doubly-curved laminated composite shells and panels with a General Higher-order Equivalent Single Layer formulation , 2013 .

[20]  Alessandro Reali,et al.  AN ISO GEOMETRIC ANALYSIS APPROACH FOR THE STUDY OF STRUCTURAL VIBRATIONS , 2006 .

[21]  Francesco Tornabene,et al.  2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution , 2011 .

[22]  Erasmo Carrera,et al.  Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method , 2014 .

[23]  Alfredo Liverani,et al.  General anisotropic doubly-curved shell theory: A differential quadrature solution for free vibrations of shells and panels of revolution with a free-form meridian , 2012 .

[24]  E. Viola,et al.  General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels , 2013 .

[25]  Elena Ferretti,et al.  GDQFEM Numerical Simulations of Continuous Mediawith Cracks and Discontinuities , 2013 .

[26]  E. Viola,et al.  Dynamical Analysis of Spherical Structural Elements Using the First-order Shear Deformation Theory , 2007 .

[27]  Chang New Chen.  Discrete Element Analysis Methods of Generic Differential Quadratures , 2006 .

[28]  Nicholas Fantuzzi,et al.  Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape , 2013 .

[29]  Zhi Zong,et al.  Advanced Differential Quadrature Methods , 2009 .

[30]  C. Shu.  Differential Quadrature and Its Application in Engineering , 2000 .

[31]  Nicholas Fantuzzi,et al.  Strong formulation finite element method for arbitrarily shaped laminated plates - Part I. Theoretical analysis , 2014 .

[32]  A. Ceruti,et al.  Free-Form Laminated Doubly-Curved Shells and Panels of Revolution Resting on Winkler-Pasternak Elastic Foundations: A 2-D GDQ Solution for Static and Free Vibration Analysis , 2013 .

[33]  J. N. Reddy,et al.  FGM and Laminated Doubly-Curved and Degenerate Shells Resting on Nonlinear Elastic Foundations: A GDQ Solution for Static Analysis with a Posteriori Stress and Strain Recovery , 2013 .

[34]  E. Viola,et al.  General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels , 2013 .

[35]  A. Ceruti,et al.  Mixed Static and Dynamic Optimization of Four-Parameter Functionally Graded Completely Doubly Curved and Degenerate Shells and Panels Using GDQ Method , 2013 .

[36]  Francesco Tornabene,et al.  Free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on Winkler–Pasternak elastic foundations , 2011 .

[37]  Erasmo Viola,et al.  Static analysis of functionally graded doubly-curved shells and panels of revolution , 2013 .