Finite element analysis

Abstract Current use of the finite element method in engineering practice is considered. The increasing use of finite element analysis in a CAD environment and factors influencing it are discussed. The technological state of the art is briefly reviewed. Special consideration is given to shell elements and solution methods, illustrating the progress being made in these and other areas of finite element technology. Future trends are predicted.

[1]  Thomas J. R. Hughes,et al.  A simple and efficient finite element for plate bending , 1977 .

[2]  R. Clough The Finite Element Method in Plane Stress Analysis , 1960 .

[3]  W. Rheinboldt,et al.  Error Estimates for Adaptive Finite Element Computations , 1978 .

[4]  M A Crisfield VARIABLE STEP-LENGTHS FOR NON-LINEAR STRUCTURAL ANALYSIS , 1982 .

[5]  A. Jennings,et al.  The solution of sparse linear equations by the conjugate gradient method , 1978 .

[6]  T. Hughes,et al.  Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element , 1981 .

[7]  O. C. Zienkiewicz,et al.  Reduced integration technique in general analysis of plates and shells , 1971 .

[8]  W. L. Wood,et al.  Comparison of Hilber‐Hughes‐Taylor and Bossak ‘α‐methods’ for the numerical integration of vibration equations , 1983 .

[9]  G. Powell,et al.  Improved iteration strategy for nonlinear structures , 1981 .

[10]  J. O. Hallquist,et al.  Recent developments in large-scale finite-element Lagrangian hydrocode technology. [Dyna 20/dyna 30 computer code] , 1981 .

[11]  M. Crisfield A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .

[12]  Paulo M. Pimenta,et al.  Thermomechanical response of solids at high strains—Natural approach , 1982 .

[13]  David R. Owen,et al.  Finite Elements in Plasticity , 1980 .

[14]  O. C. Zienkiewicz,et al.  Analysis of thick and thin shell structures by curved finite elements , 1970 .

[15]  E. Riks The Application of Newton's Method to the Problem of Elastic Stability , 1972 .

[16]  J. H. Argyris,et al.  Energy theorems and structural analysis , 1960 .

[17]  Gouri Dhatt,et al.  Incremental displacement algorithms for nonlinear problems , 1979 .

[18]  G. Strang,et al.  The solution of nonlinear finite element equations , 1979 .

[19]  B. Parlett,et al.  Lanczos versus subspace iteration for solution of eigenvalue problems , 1983 .

[20]  M. Turner Stiffness and Deflection Analysis of Complex Structures , 1956 .

[21]  O. C. Zienkiewicz,et al.  An alpha modification of Newmark's method , 1980 .

[22]  L. Lyons,et al.  A general finite element system with special reference to the analysis of cellular structures , 1977 .

[23]  F. Stummel,et al.  The limitations of the patch test , 1980 .

[24]  Ivo Babuška,et al.  A posteriori error analysis and adaptive processes in the finite element method: Part I—error analysis , 1983 .

[25]  J. M. Corum Verification and qualification of inelastic analysis computer programs , 1975 .

[26]  Werner C. Rheinboldt,et al.  Adaptive mesh refinement processes for finite element solutions , 1981 .

[27]  Richard H. Macneal,et al.  A simple quadrilateral shell element , 1978 .

[28]  M. Crisfield,et al.  A faster modified newton-raphson iteration , 1979 .

[29]  Isaac Fried,et al.  Shear in C0 and C1 ending finite elements , 1973 .

[30]  W. R. Buell,et al.  Mesh Generation—A Survey , 1973 .

[31]  Robert J. Melosh,et al.  A Stiffness Matrix for the Analysis of Thin Plates in Bending , 1961 .

[32]  R. D. Krieg,et al.  Accuracies of Numerical Solution Methods for the Elastic-Perfectly Plastic Model , 1977 .

[33]  Thomas J. R. Hughes,et al.  Improved numerical dissipation for time integration algorithms in structural dynamics , 1977 .

[34]  Thomas J. R. Hughes,et al.  An improved treatment of transverse shear in the mindlin-type four-node quadrilateral element , 1983 .

[35]  E. Riks An incremental approach to the solution of snapping and buckling problems , 1979 .

[36]  M. Crisfield A four-noded thin-plate bending element using shear constraints—a modified version of lyons' element , 1983 .

[37]  Bruce M. Irons,et al.  An engineers' defence of the patch test , 1983 .