Analysis and modeling in mechanics: An informal view

Abstract In the context of the maturation of finite element methodology this paper reviews solution approaches that combine classical analytical techniques with computer-based numerical methods. Developments in boundary integral equations, asymptotic postbuckling analysis, and limit point analysis are touched upon, as are some aspects of structural modeling. Emphasis is also placed on the importance of understanding both the scope and limitations of a particular structural model. This understanding has implications for the educator as well as for the researcher and the practicing engineer.

[1]  Clive L. Dym,et al.  STABILITY THEORY AND ITS APPLICATIONS TO STRUCTURAL MECHANICS , 1974 .

[2]  G. A. Thurston.  Continuation of Newton’s Method Through Bifurcation Points , 1969 .

[3]  R. Archer.  Stability limits for a clamped spherical shell segment under uniform pressure , 1958 .

[4]  Bending waves in shells , 1977 .

[5]  Bernard Budiansky,et al.  BUCKLING OF CLAMPED SHALLOW SPHERICAL SHELLS , 1959 .

[6]  Raphael T. Haftka,et al.  Adaption of Koiter's method to finite element analysis of snap-through buckling behavior† , 1971 .

[7]  John W. Hutchinson,et al.  Comment on "Effect of Nonlinear Prebuckling State on the Postbuckling Behavior and Imperfection-Sensitivity of Elastic Structures" , 1969 .

[8]  A. L. Hale,et al.  On the Substructure Synthesis Method , 1981 .

[9]  Charles R. Steele,et al.  A geometric optics solution for the thin shell equation , 1971 .

[10]  Irving H. Shames,et al.  Solid mechanics: a variational approach , 1973 .

[11]  Ted Belytschko,et al.  Nonlinear Processes in Engineering , 1975 .

[12]  T. Y. Na,et al.  Computational methods in engineering boundary value problems , 1979 .

[13]  Clive L. Dym,et al.  Vibration : beams, plates, and shells , 1976 .

[14]  G. A. Thurston.  Newton's method: A link between continuous and discrete solutions of nonlinear problems , 1980 .

[15]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[16]  P. Stehlin,et al.  Use of global functions for improvement in efficiency of nonlinear analysis. [in computer structural displacement estimation , 1981 .

[17]  David Bushnell,et al.  Buckling of Shells-Pitfall for Designers , 1981 .

[18]  David Bushnell,et al.  Computerized analysis of shells-governing equations , 1984 .

[19]  G. Cohen.  Reply by Author to J.R. Fitch and J.W. Hutchinson , 1969 .

[20]  P. Stern,et al.  Automatic choice of global shape functions in structural analysis , 1978 .

[21]  A. Kalnins,et al.  Analysis of Shells of Revolution Subjected to Symmetrical and Nonsymmetrical Loads , 1964 .

[22]  John W. Hutchinson,et al.  Dynamic buckling of imperfection-sensitive structures , 1966 .

[23]  Leonard Meirovitch,et al.  A general substructure synthesis method for the dynamic simulation of complex structures , 1980 .

[24]  W. Hurty.  Dynamic Analysis of Structural Systems Using Component Modes , 1965 .

[25]  P Tong.  COMPUTATIONAL METHODS IN GROUND TRANSPORTATION , 1976 .

[26]  G. A. Cohen,et al.  FASOR—A second generation shell of revolution code , 1979 .

[27]  J. Harvey Evans,et al.  Ocean engineering structures , 1969 .

[28]  H. Weitzner,et al.  Perturbation Methods in Applied Mathematics , 1969 .

[29]  Forman S. Acton,et al.  Numerical methods that work , 1970 .

[30]  Leonard Meirovitch,et al.  Computational Methods in Structural Dynamics , 1980 .

[31]  T. A. Cruse,et al.  Advanced applications of boundary-integral equation methods☆ , 1978 .

[32]  G. A. Cohen.  Effect of a nonlinear prebuckling state on the postbuckling behaviorand imperfect on sensitivity of elastic structures. , 1968 .

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

[34]  W. T. Koiter.  THE STABILITY OF ELASTIC EQUILIBRIUM , 1970 .

[35]  Richard L. Meehan.  Getting Sued and Other Tales of the Engineering Life , 1981 .

[36]  Ahmed K. Noor,et al.  SURVEY OF COMPUTER PROGRAMS FOR SOLUTION OF NONLINEAR STRUCTURAL AND SOLID MECHANICS PROBLEMS , 1981 .

[37]  T. Cruse,et al.  Boundary-integral equation analysis of cracked anisotropic plates , 1975 .

[38]  G. M. L. Gladwell,et al.  Branch mode analysis of vibrating systems , 1964 .

[39]  A. Mendelson,et al.  Application of boundary integral method to elastoplastic analysis of V-notched beams , 1975 .

[40]  G. A. Thurston.  Newton’s Method Applied to Problems in Nonlinear Mechanics , 1965 .

[41]  Clive L. Dym,et al.  Principles of mathematical modeling , 1980 .

[42]  G. A. Thurston.  A Numerical Solution of the Nonlinear Equations for Axisymmetric Bending of Shallow Spherical Shells , 1961 .

[43]  G. A. Cohen.  Computer program for analysis of imperfection sensitivity of ring stiffened shells of revolution , 1971 .

[44]  J. Z. Zhu,et al.  The finite element method , 1977 .

[45]  R. Archer.  On the Numerical Solution of the Nonlinear Equations for Shells of Revolution , 1962 .

[46]  David Bushnell,et al.  BIFURCATION BUCKLING OF SHELLS OF REVOLUTION INCLUDING LARGE DEFLECTIONS, PLASTICITY AND CREEP , 1974 .

[47]  Melvin S. Anderson.  Buckling of Periodic Lattice Structures , 1981 .

[48]  Clive L. Dym,et al.  Introduction to the theory of shells , 1974 .

[49]  C. Steele,et al.  Nonlinear Corrections for Edge Bending of Shells , 1980 .

[50]  Arturs Kalnins.  Numerical methods for mixed boundary value problems of shells of revolution , 1972 .