Exact and Approximate Static Structural Reanalysis

The ‘exact’ and approximate methods of structural re-analysis are reviewed in this chapter. With the advent of less expensive computing hardware, structural engineers are employing optimization and non-linear analysis techniques in new application areas which require more computational power hence re-analysis techniques are likely to become more important over the next decade.

[1]  H. Miura,et al.  An approximate analysis technique for design calculations , 1971 .

[2]  Richard H. Gallagher,et al.  Approximate force method reanalysis techniques in structural optimization , 1985 .

[3]  E. D. Poppleton,et al.  The Redesign of Redundant Structures Having Undesirable Stress Distributions , 1961 .

[4]  R. J. Melosh,et al.  Multiple Configuration Analysis of Structures , 1968 .

[5]  Steven J. Fenves,et al.  Sparse Matrices, Graph Theory, and Reanalysis , 1981 .

[6]  A. Householder.  A Survey of Some Closed Methods for Inverting Matrices , 1957 .

[7]  J. M. Bennett.  Triangular factors of modified matrices , 1965 .

[8]  Alex L. M. Grzedzielski,et al.  Note on Some Applications of the Matrix Force Method of Structural Analysis , 1960, The Journal of the Royal Aeronautical Society.

[9]  M. Powell,et al.  On the Modification of LDL T Factorizations , 1974 .

[10]  K. I. Majid,et al.  The elastic–plastic analysis of frames by the theorems of structural variation , 1985 .

[11]  Jaroslaw Sobieszczanski.  Structural Modification by Perturbation Method , 1968 .

[12]  R. J. Melosh,et al.  APPROXIMATE MULTIPLE CONFIGURATION ANALYSIS AND ALLOCATION FOR LEAST WEIGHT STRUCTURAL DESIGN. , 1967 .

[13]  Leonard Spunt,et al.  Optimum structural design , 1971 .

[14]  Uri Kirsch,et al.  Approximate structural reanalysis for optimization along a line , 1982 .

[15]  J. Sherman,et al.  Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix , 1950 .

[16]  K. M. Romstad,et al.  Design parameter variation and structural response , 1973 .

[17]  Olaf O. Storaasli,et al.  On the Accuracy of the Taylor Approximation for Structure Resizing , 1974 .

[18]  P. Gill,et al.  Methods for computing and modifying the $LDV$ factors of a matrix , 1975 .

[19]  Uri Kirsch,et al.  On some simplified models for optimal design of structural systems , 1985 .

[20]  K. Kavanagh,et al.  An approximate algorithm for the reanalysis of structures by the finite element method , 1972 .

[21]  O. O. Storaasli,et al.  Design oriented structural analysis. , 1973 .

[22]  Graham H. Powell,et al.  Solution of progressively changing equilibrium equations for nonlinear structures , 1977 .

[23]  U. Kirsch,et al.  Approximate Behavior Models for Optimum Structural Design , 1981 .

[24]  L. Schmit,et al.  Some Approximation Concepts for Structural Synthesis , 1974 .

[25]  Barry Hilary Valentine Topping,et al.  Static Reanalysis: A Review , 1987 .

[26]  Barry Hilary Valentine Topping,et al.  The application of the theorems of structural variation to finite element problems , 1983 .

[27]  K. J. Zlmmermann,et al.  Interactive use of finite element programs—or—how to get more out of your finite element model , 1980 .

[28]  R. H. MacNeal,et al.  Application of the Compensation Theorem to the Modification of Redundant Structures , 1953 .

[29]  E. Kosko,et al.  Effect of Local Modifications in Redundant Structures , 1954 .

[30]  Alex. L. M. Grzedzielski,et al.  The Initial Strain Concept , 1961, The Journal of the Royal Aeronautical Society.

[31]  Uri Kirsch,et al.  Structural reanalysis by iteration , 1972 .

[32]  B. Topping,et al.  The theorems of geometric variation for finite element analysis , 1988 .

[33]  Jaroslaw Sobieszczanski,et al.  Matrix algorithm for structural modification based upon the parallelelement concept , 1969 .

[34]  Kumar G. Bhatia,et al.  Rapid iterative reanalysis for automated design , 1973 .

[35]  Kincho H. Law,et al.  Sparse matrix factor modification in structural reanalysis , 1985 .

[36]  P. Morse,et al.  Principles of Numerical Analysis , 1954 .

[37]  Richard N. Wright,et al.  Solving topologically modified structures , 1973 .

[38]  A. Pipano,et al.  Efficient reanalysis of structures by a direct modification method. [local stiffness modifications of large structures , 1976 .

[39]  John Argyris,et al.  A direct modification procedure for the displacement method , 1971 .

[40]  Uri Kirsch,et al.  Optimal Design Based on Approximate Scaling , 1982 .

[41]  W. J. Goodey.  Solution of Modified Linear Simultaneous Equations , 1959 .

[42]  The theorems of geometric variation for nonlinear finite element analysis , 1987 .

[43]  W. J. Goodey.  Notes on a General Method of Treatment of Structural Discontinuities , 1955 .

[44]  Erdal Atrek,et al.  Theorems of structural variation: a simplification , 1985 .

[45]  W D Pilkey,et al.  Efficient Reanalysis of Locally Modified Structures. , 1980 .

[46]  P. C. Das.  Reanalysing structures with small modifications , 1978 .

[47]  Dwc Elliott,et al.  TOPOLOGICAL DESIGN OF PIN JOINTED STRUCTURES BY NON-LINEAR PROGRAMMING. , 1973 .

[48]  William G. Sullivan.  A review of: “APPLIED FORECASTING METHODS” by N. T. Thomopoulos, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, iiv + 369 pages, list $24.50 , 1979 .

[49]  R. L. Sack,et al.  Modification of elements in the displacement method. , 1967 .

[50]  J. Arora.  Survey of Structural Reanalysis Techniques , 1976 .

[51]  Ahmed K. Noor,et al.  Reduced Basis Technique for Nonlinear Analysis of Structures , 1980 .

[52]  Uri Kirsch,et al.  Reanalysis for Limited Structural Design Modifications , 1972 .

[53]  Suresh R. Phansalkar.  Matrix iterative methods for structural reanalysis , 1974 .

[54]  E. D. Poppleton.  Note on the design of redundant structures , 1960 .

[55]  Ahmed K. Noor,et al.  Approximate Reanalysis Techniques with Substructuring , 1975 .

[56]  Barry Hilary Valentine Topping,et al.  The use and efficiency of the theorems of structural variation for finite element analysis , 1987 .

[57]  M. A. E. Bakry.  Optimal design of transmission line towers , 1977 .

[58]  Ahmed K. Noor,et al.  Structural reanalysis via a mixed method , 1975 .

[59]  Alston S. Householder,et al.  The Theory of Matrices in Numerical Analysis , 1964 .

[60]  K I Majid,et al.  Optimum design of structures , 1974 .

[61]  Sebastian von Hoerner.  Homologous Deformations of Tiltable Telescopes , 1967 .

[62]  Wei H. Yang.  A method for updating Cholesky factorization of a band matrix , 1977 .

[63]  Ahmed K. Noor,et al.  Multiple Configuration Analysis Via Mixed Method , 1974 .

[64]  B. H. V. Topping,et al.  The application of dynamic relaxation to the design of modular space structures , 1978 .

[65]  Kyung K. Choi,et al.  A sparse matrix finite element technique for iterative structural optimization , 1983 .

[66]  H. F. Michielsen.  Structural Modifications in Redundant Structures , 1953 .

[67]  B. P. Wang,et al.  REANALYSIS, MODAL SYNTHESIS AND DYNAMIC DESIGN. , 1983 .

[68]  Mehmet Polat Saka,et al.  THE THEOREMS OF STRUCTURAL VARIATION GENERALIZED FOR RIGIDLY JOINTED FRAMES. , 1978 .

[69]  Gilbert C. Best.  The Stress-Area Method Applied to Frames , 1946 .

[70]  G. Best,et al.  A METHOD OF STRUCTURAL WEIGHT MINIMIZATION SUITABLE FOR HIGH-SPEED DIGITAL COMPUTERS , 1963 .

[71]  Gerhard Zielke,et al.  Inversion of Modified Symmetric Matrices , 1968, JACM.

[72]  William W. Hager,et al.  Updating the Inverse of a Matrix , 1989, SIAM Rev..

[73]  S. Kelsey,et al.  Initial Strains in the Matrix Force Method of Structural Analysis , 1960, The Journal of the Royal Aeronautical Society.

[74]  Eryk Kosko.  Matrix Inversion by Partitioning , 1957 .

[75]  Ahmed K. Noor,et al.  Nonlinear analysis via global–local mixed finite element approach , 1980 .

[76]  Michał Kleiber,et al.  Modified triangular factors in the incremental finite element analysis with nonsymmetric stiffness changes , 1978 .

[77]  B H V Topping,et al.  THEOREMS OF GEOMETRIC VARIATION FOR ENGINEERING STRUCTURES. , 1989 .

[78]  J. L. Meek.  Matrix Structural Analysis , 1971 .

[79]  John E. Brock.  Variation of coefficients of simultaneous linear equations , 1953 .

[80]  B. Topping.  THE THEOREMS OF STRUCTURAL AND GEOMETRIC VARIATION: A REVIEW , 1987 .

[81]  Uri Kirsch,et al.  Approximate structural reanalysis based on series expansion , 1981 .

[82]  John Argyris,et al.  General Treatment of Structural Modifications , 1972 .

[83]  A. Noor.  Recent advances in reduction methods for nonlinear problems. [in structural mechanics , 1981 .

[84]  Ahmed K. Noor,et al.  Approximate techniques of strctural reanalysis , 1974 .

[85]  B. P. Wang,et al.  Parameterization in Finite Element Analysis , 1981 .

[86]  Bo Ping Wang,et al.  An efficient zooming method for finite element analysis , 1984 .

[87]  Graham H. Powell,et al.  Efficient Reanalysis of Modified Structures , 1970 .

[88]  P. Cicala,et al.  Effects of Cutouts in Semimonocoque Structures , 1948 .

[89]  E. F. Kurtz,et al.  Matrix methods in elastomechanics , 1963 .

[90]  J. J. Modi,et al.  The re-analysis of linear structures on serial and parallel computers , 1991 .

[91]  G. C. Best,et al.  The Stress-Area Method of Designing Beams , 1945 .

[92]  C. D. Mote,et al.  Optimization methods for engineering design , 1971 .