An improved accelerated initial stress procedure for elasto-plastic finite element analysis

The most flexible and generally applicable methods for elasto-plastic analysis are those based on an incremental-iterative form of the initial stress approach, but such methods often exhibit slow convergence. The acceleration procedure known as the alpha-constant stiffness method is reconsidered and some modifications are proposed. The principal difference in the present approach lies in the use of a single acceleration parameter, rather than a diagonal matrix of acceleration coefficients. The new scheme shows a significant improvement in numerical stability and converges three times faster than the standard initial stress method. Some practical aspects associated with the method are discussed and a number of applications are presented.

[1]  E. H. Brown.  A theory for the mechanical behaviour of sand , 1966 .

[2]  K. Lo,et al.  Stress analysis and slope stability in strain-softening materials , 1973 .

[3]  Alan Jennings,et al.  Matrix Computation for Engineers and Scientists , 1977 .

[4]  R. Hill.  The mathematical theory of plasticity , 1950 .

[5]  J. Rice,et al.  The growth of slip surfaces in the progressive failure of over-consolidated clay , 1973, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[6]  O. C. Zienkiewicz,et al.  Elasto‐plastic solutions of engineering problems ‘initial stress’, finite element approach , 1969 .

[7]  Ian P. King,et al.  Elastic-plastic analysis of two-dimensional stress systems by the finite element method , 1967 .

[8]  J. Prévost,et al.  Soil mechanics and plasticity analysis of strain softening , 1975 .

[9]  O. C. Zienkiewicz,et al.  Note on the ‘Alpha’‐constant stiffness method for the analysis of non‐linear problems , 1972 .

[10]  A. Mendelson.  Plasticity: Theory and Application , 1968 .

[11]  K. Washizu.  Variational Methods in Elasticity and Plasticity , 1982 .

[12]  O. C. Zienkiewicz,et al.  Curved, isoparametric, “quadrilateral” elements for finite element analysis , 1968 .

[13]  O. C. Zienkiewicz,et al.  Elasto‐plastic stress analysis. A generalization for various contitutive relations including strain softening , 1972 .

[14]  Wai-Fah Chen.  Limit Analysis and Soil Plasticity , 1975 .

[15]  R. Lewis,et al.  Associated and non-associated visco-plasticity and plasticity in soil mechanics , 1975 .

[16]  J. Argyris,et al.  Elasto-plastic Matrix Displacement Analysis of Three-dimensional Continua , 1965, The Journal of the Royal Aeronautical Society.

[17]  John Argyris,et al.  Methods of elastoplastic analysis , 1972 .

[18]  I. M. Smith,et al.  Incremental Numerical Solution of a Simple Deformation Problem in Soil Mechanics , 1970 .

[19]  Chandrakant S. Desai,et al.  Numerical Methods in Geotechnical Engineering , 1979 .

[20]  William Prager,et al.  Recent Developments in the Mathematical Theory of Plasticity , 1949 .

[21]  W. A. Marr,et al.  Incremental plasticity analysis of frictional soils , 1977 .

[22]  D. C. Drucker,et al.  Soil mechanics and plastic analysis or limit design , 1952 .

[23]  Stein Sture,et al.  Strain‐softening of brittle geologic materials , 1978 .

[24]  O. C. Zienkiewicz,et al.  Some useful forms of isotropic yield surfaces for soil and rock mechanics , 1977 .

[25]  P. Marcal,et al.  Introduction to the Finite-Element Method , 1973 .

[26]  Y. Yamada,et al.  Plastic stress-strain matrix and its application for the solution of elastic-plastic problems by the finite element method , 1968 .