摘要:

AbstractThis paper considers the problem of integrating the constitutive relations for Tresca and Mohr–Coulomb materials under conditions of plane strain. In the case of a Tresca material, we show that the constitutive law may be integrated exactly by assuming the strain rates dϵ/dλ to be constant. We also derive a semi‐analytic method for integrating both types of constitutive law which assumes that the quantities dϵ/dλ are constant. This approach is motivated by the fact that the exact variation of the strains during a time interval is unknown and leads to a single non‐linear equation in λ which can be solved efficiently to yield the unknown stresses. Finally, we compare the results from the analytic and semi‐analytic methods with those from a variety of numerical integra

ISSN:0029-5981    

DOI:10.1002/nme.1620330112

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe theory of optimal control and the theory of a substructural chain in static structural analysis are mutually simulated issues. From the minimum potential energy variational principle of the substructural chain, the generalized variational principle with two kinds of variables is derived first. By comparing that generalized variational principle with the variational principle in LQ control theory, the simulation relation is established. Based on that relation, the potential energy and mixed energy formulation of the algebraic Riccati equations are derived, then iterative algorithms are proposed which give the upper and lower bounds to the solution matrix. By using the solutions of the positive and negative co‐ordinate algebraic Riccati equations, the canonical transformation matrices for the eigenproblems of the substructural chain and LQ control are constructed respectively, which reduce the eigenproblem to half‐size. The properties of the solutions are analysed, which establishes the basis for expansion soluti

ISSN:0029-5981    

DOI:10.1002/nme.1620330113

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620330114

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620330115

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620330116

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620330117

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620330118

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620330101

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY