3.12 – Direct Methods of Limit and Shakedown Analysis

[1]  G. Dvorak,et al.  Shakedown of unidirectional composites , 1975 .

[2]  S. Karadeniz,et al.  The influence of transient thermal loading on the Bree plate; A simplified method of analysis , 1984 .

[3]  R. Seshadri,et al.  On relating the reference stress, limit load and the ASME stress classification concepts , 1993 .

[4]  A. Ponter.  Minimum Theorems and Iterative Solutions Methods for Creep Cyclic Loading Problems , 2001 .

[5]  Alan R.S. Ponter,et al.  Shakedown state simulation techniques based on linear elastic solutions , 1997 .

[6]  Giulio Maier,et al.  Dynamic non-shakedown theorem for elastic perfectly-plastic continua , 1974 .

[7]  J. Bree.  Elastic-plastic behaviour of thin tubes subjected to internal pressure and intermittent high-heat fluxes with application to fast-nuclear-reactor fuel elements , 1967 .

[8]  Francis Tin-Loi.  A Yield Surface Linearization Procedure in Limit Analysis , 1990 .

[9]  Alan R.S. Ponter,et al.  The Plastic Ratcheting of Thin Cylindrical Shells Subjected to Axisymmetric Thermal and Mechanical Loading , 1987 .

[10]  Giulio Maier,et al.  Dynamic shakedown and bounding theory for a class of nonlinear hardening discrete structural models , 1990 .

[11]  R. Seshadri,et al.  Limit Loads of Mechanical Components and Structures Using the GLOSS R-Node Method , 1992 .

[12]  F. Tin-Loi,et al.  SHAKEDOWN OF FRAMES WITH SEMIRIGID CONNECTIONS , 1993 .

[13]  José Herskovits,et al.  A two-stage feasible directions algorithm for nonlinear constrained optimization , 1981, Math. Program..

[14]  Alan R.S. Ponter,et al.  Limit state solutions, based upon linear elastic solutions with a spatially varying elastic modulus , 1997 .

[15]  G. Maier.  A shakedown matrix theory allowing for workhardening and second-order geometric effects , 1974 .

[16]  Castrenze Polizzotto,et al.  On the Conditions to Prevent Plastic Shakedown of Structures: Part I—Theory , 1993 .

[17]  I. Roman,et al.  ON SHAKEDOWN OF ELASTIC PLASTIC BODIES WITH BRITTLE DAMAGE , 2000 .

[18]  Dimitris C. Lagoudas,et al.  FATIGUE DAMAGE AND SHAKEDOWN IN METAL MATRIX COMPOSITE LAMINATES , 1994 .

[19]  A. Gurson.  Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media , 1977 .

[20]  J. Mandel.  Adaptation d'une structure plastique ecrouissable et approximations , 1976 .

[21]  Michele Capurso.  Some Upper Bound Principles to Plastic Strains in Dynamic Shakedown of Elastoplastic Structures , 1979 .

[22]  B. G. Neal.  Plastic Collapse and Shakedown Theorems for Structures of Strain-Hardening Material , 1950 .

[23]  D. Weichert.  On the influence of geometrical nonlinearities on the shakedown of elastic-plastic structures , 1986 .

[24]  Paolo Fuschi,et al.  Limit analysis for a general class of yield conditions , 2000 .

[25]  W. T. Koiter.  General theorems for elastic plastic solids , 1960 .

[26]  Erwin Stein,et al.  Modeling and computation of shakedown problems for nonlinear hardening materials , 1993 .

[27]  Giulio Maier,et al.  Static shakedown theorems in piecewise linearized poroplasticity , 1998 .

[28]  Jan A. König,et al.  A finite element formulation for shakedown problems using a yield criterion of the mean , 1976 .

[29]  Giulio Maier.  Shakedown of Plastic Structures with Unstable Parts , 1972 .

[30]  H. Stumpf.  Theoretical and computational aspects in the shakedown analysis of finite elastoplasticity , 1993 .

[31]  Alternative approach to shakedown as a solution of a min-max problem , 1992 .

[32]  John Lysmer,et al.  LIMIT ANALYSIS OF PLANE PROBLEMS IN SOIL MECHANICS , 1970 .

[33]  J. A. König.  On exactness of the kinematical approach in the structural shakedown and limit analysis , 1982 .

[34]  Alan R.S. Ponter,et al.  Shakedown Limits for a General Yield Condition: Implementation and Application for a Von Mises Yield Condition , 2000 .

[35]  J. Pastor,et al.  Mise en oeuvre numerique des methodes de l'analyse limite pour les materiaux de von mises et de Coulomb standards en deformation plane , 1976 .

[36]  J. Tinsley Oden,et al.  A posteriori error estimator and adaptive procedures for computation of shakedown and limit loads on pressure vessels , 1997 .

[37]  J. Zarka,et al.  Elastic-Plastic Response of a Structure to Cyclic Loading: Practical Rules , 1981 .

[38]  J. Orkisz,et al.  Analysis of residual stresses at shakedown: A hybrid approach , 1988 .

[39]  Olivier Coussy,et al.  Poroplastic analysis of concrete dams and their foundations , 1991 .

[40]  E. Stein,et al.  Shakedown of a cracked body consisting of kinematic hardening material , 1996 .

[41]  D. Weichert,et al.  Elastic-plastic shells under variable mechanical and thermal loads , 1992 .

[42]  Michele Capurso.  Limit analysis of continuous media with piecewise linear yeld condition , 1971 .

[43]  Scott W. Sloan,et al.  Lower bound limit analysis using non‐linear programming , 2002 .

[44]  Shakedown theorems in poroplastic dynamics , 2002 .

[45]  Arkadi Nemirovski,et al.  On Polyhedral Approximations of the Second-Order Cone , 2001, Math. Oper. Res..

[46]  Pedro Ponte Castañeda,et al.  Yield criteria for porous media in plane strain: second-order estimates versus numerical results , 2002 .

[47]  D. Weichert,et al.  On kinematic upper bounds for the safety factor in shakedown theory , 1992 .

[48]  G. Maier,et al.  On Some Issues in Shakedown Analysis , 2001 .

[49]  Lahbib Bousshine,et al.  Limit analysis theorems for implicit standard materials: Application to the unilateral contact with dry friction and the non-associated flow rules in soils and rocks , 1998 .

[50]  R. Seshadri,et al.  The Generalized Local Stress Strain (GLOSS) Analysis—Theory and Applications , 1991 .

[51]  D. Weichert.  Shakedown at finite displacements; A note on Melan's theorem , 1984 .

[52]  M. Janas,et al.  A min-max procedure for the shakedown analysis of skeletal structures , 1995 .

[53]  Francesco Genna.  A nonlinear inequality, finite element approach to the direct computation of shakedown load safety factors , 1988 .

[54]  Ming-Wan Lu,et al.  An algorithm for plastic limit analysis , 1995 .

[55]  Alberto Taliercio,et al.  Lower and upper bounds to the macroscopic strength domain of a fiber-reinforced composite material , 1992 .

[56]  G. Maier,et al.  Bounds on Plastic Strains and Displacements in Dynamic Shakedown of Work-Hardening Structures , 1974 .

[57]  W. Prager.  Limit analysis: the development of a concept , 1974 .

[58]  Giulio Maier,et al.  Numerical shakedown analysis of periodic heterogeneous materials by a kinematic approach , 1998 .

[59]  Michał Kleiber,et al.  On a numerical approach to shakedown analysis of structures , 1980 .

[60]  Giulio Maier,et al.  Shakedown theorems for some classes of nonassociative hardening elastic-plastic material models , 1995 .

[61]  Castrenze Polizzotto.  A convergent bounding principle for a class of elastoplastic strain-hardening solids , 1986 .

[62]  V. Tvergaard.  Influence of voids on shear band instabilities under plane strain conditions , 1981 .

[63]  Dieter Weichert,et al.  An extension of the static shakedown theorem to inelastic cracked structures , 1999 .

[64]  Ernst Melan,et al.  Zur Plastizität des räumlichen Kontinuums , 1938 .

[65]  J. Ju,et al.  On energy-based coupled elastoplastic damage theories: Constitutive modeling and computational aspects , 1989 .

[66]  Giulio Maier,et al.  Inadaptation theorems in the dynamics of elastic-work hardening structures , 1973 .

[67]  J. Mandel,et al.  Adaptation d'une structure elastoplastique a ecrouissage cinematique , 1977 .

[68]  Dieter Weichert,et al.  Inelastic behaviour of structures under variable repeated loads : direct analysis methods , 2002 .

[69]  Castrenze Polizzotto,et al.  Dynamic shakedown by modal analysis , 1984 .

[70]  Haofeng Chen,et al.  A method for the evaluation of a ratchet limit and the amplitude of plastic strain for bodies subjected to cyclic loading , 2001 .

[71]  Giulio Maier,et al.  Kinematic Limit Analysis of Periodic Heterogeneous Media , 2000 .

[72]  Francesco Genna.  Bilateral bounds for structures under dynamic shakedown conditions , 1991 .

[73]  J. L. Silveira,et al.  On extremum principles and algorithms for shakedown analysis , 1997 .

[74]  J. Tirosh.  The dual shakedown conditions for dilute fibrous composites , 1998 .

[75]  J. Herskovits.  Feasible Direction Interior-Point Technique for Nonlinear Optimization , 1998 .

[76]  Yun-Feng Dong,et al.  Dynamic shakedown theory of elastoplastic work-hardening structures allowing for second-order geometric effects , 1993 .

[77]  Strainhardening effects in shakedown processes , 1988 .

[78]  Upper bound methods for use in the design and assessment of axisymmetric thin shells subjected to cyclic thermal loading , 1989 .

[79]  Alan R.S. Ponter,et al.  A general approximate technique for the finite element shakedown and limit analysis of axisymmetrical shells. Part 2: Numerical applications , 1997 .

[80]  Dieter Weichert,et al.  Numerical shakedown analysis of damaged structures , 1998 .

[81]  P. M. Naghdi,et al.  A general theory of an elastic-plastic continuum , 1965 .

[82]  Xi-Qiao Feng,et al.  Damage and shakedown analysis of structures with strain-hardening , 1995 .

[83]  P. de Buhan,et al.  A comprehensive stability analysis of soil nailed structures , 1993 .

[84]  Donald Mackenzie,et al.  A method of estimating limit loads by iterative elastic analysis. II—Nozzle sphere intersections with internal pressure and radial load , 1992 .

[85]  D. Weichert,et al.  Application of shakedown theory to soils with non associated flow rules , 1997 .

[86]  E. Stein,et al.  An analytical method for shakedown problems with linear kinematic hardening materials , 1994 .

[87]  Robert Hamilton,et al.  The elastic compensation method for limit and shakedown analysis: A review , 2000 .

[88]  S. Caddemi,et al.  Theorems of restricted dynamic shakedown , 1993 .

[89]  D. Weichert,et al.  Influence of geometrical nonlinearities on the shakedown of damaged structures , 1998 .

[90]  Giulio Maier,et al.  Shakedown theory in perfect elastoplasticity with associated and nonassociated flow-laws: A finite element, linear programming approach , 1969 .

[91]  B. Nayroles,et al.  La notion de sanctuaire d'élasticité et d'adaptation des structures , 1993 .

[92]  S. Karadeniz,et al.  An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loading, Part 2: Applications , 1985 .

[93]  Paolo Fuschi,et al.  Shakedown of Structures Subjected to Dynamic External Actions and Related Bounding Techniques , 2002 .

[94]  C. Polizzotto,et al.  Shakedown and steady-state responses of elastic-plastic solids in large displacements , 1996 .

[95]  J. Groß-Weege.  A unified formulation of statical shakedown criteria for geometrically nonlinear problems , 1990 .

[96]  Dieter Weichert,et al.  Application of shakedown theory to damaging inelastic material under mechanical and thermal loads , 1997 .

[97]  Haofeng Chen,et al.  A minimum theorem for cyclic load in excess of shakedown, with application to the evaluation of a ratchet limit , 2001 .

[98]  G. Jiang.  Non‐linear finite element formulation of kinematic limit analysis , 1995 .

[99]  A. Sawczuk.  Evaluation of upper bounds to shakedown loads for shells , 1969 .

[100]  S. Karadeniz,et al.  A linear programming upper bound approach to the shakedown limit of thin shells subjected to variable thermal loading , 1984 .

[101]  Joseph Pastor,et al.  New bounds for the height limit of a vertical slope , 2000 .

[102]  L. Corradi,et al.  Mathematical programming methods for displacement bounds in elasto-plastic dynamics☆ , 1976 .

[103]  Bernhard A. Schrefler,et al.  Mechanics and thermodynamics of saturated/unsaturated porous materials and quantitative solutions* , 2002 .

[104]  S. Schmauder,et al.  Transverse strength of continuous fiber metal matrix composites , 1994 .

[105]  En-Jui Lee.  Elastic-Plastic Deformation at Finite Strains , 1969 .

[106]  A comparative study of bounding techniques in dynamic shakedown of elasto‐plastic structures , 1974 .

[107]  Giulio Maier,et al.  Shakedown analysis in poroplasticity by linear programming , 2000 .

[108]  Castrenze Polizzotto.  A Study on Plastic Shakedown of Structures: Part I—Basic Properties , 1993 .

[109]  P. D. Chinh.  An Upper Bound Kinematic Approach to the Shakedown Analysis of Structures , 1999 .

[110]  Alberto Corigliano,et al.  Dynamic shakedown analysis and bounds for elastoplastic structures with nonassociative, internal variable constitutive laws , 1995 .

[111]  V. Carvelli,et al.  Shakedown analysis of defective pressure vessels by a kinematic approach , 1999 .

[112]  Yuzhe Liu,et al.  A numerical method for plastic limit analysis of 3-D structures , 1995 .

[113]  G. Maier,et al.  Upper Bounds on Deformations of Elastic-Workhardening Structures in the Presence of Dynamic and Second-Order Geometric Effects∗ , 1973 .

[114]  Haofeng Chen,et al.  Shakedown and limit analyses for 3-D structures using the linear matching method , 2001 .

[115]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, Comb..

[116]  J. Kamenjarzh,et al.  On kinematic method in shakedown theory. I: Duality of extremum problems , 1994 .

[117]  J. Lemaître.  A CONTINUOUS DAMAGE MECHANICS MODEL FOR DUCTILE FRACTURE , 1985 .

[118]  Alberto Corigliano,et al.  Dynamic shakedown in elastoplastic structures with general internal variable constitutive laws , 1991 .

[119]  Radoslaw L. Michalowski,et al.  SLOPE STABILITY ANALYSIS: A KINEMATICAL APPROACH , 1995 .

[120]  SECTION 10.8 – Limit and Shakedown Analysis of Periodic Heterogeneous Media , 2001 .

[121]  Scott W. Sloan,et al.  Upper bound limit analysis using linear finite elements and non‐linear programming , 2001 .

[122]  S. Karadeniz,et al.  An Extended Shakedown Theory for Structures That Suffer Cyclic Thermal Loading, Part 1: Theory , 1985 .

[123]  A.R.S. Ponter.  General displacement and work bounds for dynamically loaded bodies , 1975 .

[124]  Alan R.S. Ponter,et al.  A general approximate technique for the finite element shakedown and limit analysis of axisymmetrical shells. Part 1: Theory and fundamental relations , 1997 .

[125]  Giulio Ceradini,et al.  Dynamic Shakedown in Elastic-Plastic Bodies , 1980 .

[126]  D. Weichert,et al.  The numerical assessment of elastic-plastic sheets under variable mechanical and thermal loads using a simplified two-surface yield condition , 1988 .

[127]  G. Maier.  A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes , 1970 .

[128]  José Herskovits,et al.  An iterative algorithm for limit analysis with nonlinear yield functions , 1993 .