AN EFFICIENT ALGORITHM FOR THE COMPUTATION OF STABILITY POINTS OF DYNAMICAL SYSTEMS UNDER STEP LOAD

Many engineering structures exhibit loss of stability under static and dynamic loading. Due to the significance of these phenomena in engineering design this topic has attracted considerable attention during the last decades. In recent years much effort has been made to devise algorithms within finite element analysis to investigate the static stability behaviour of structures. With these methods stable and unstable paths can be traced, and limit or bifurcation points can be computed efficiently. The associated arc‐length or branch‐switching procedures are today standard tools in existing finite element codes.

[1]  Peter Wriggers,et al.  A general procedure for the direct computation of turning and bifurcation points , 1990 .

[2]  W. Krätzig,et al.  Eine einheitliche statische und dynamische Stabilitätstheorie für Pfadverfolgungsalgorithmen in der numerischen Festkörpermechanik , 1989 .

[3]  Michał Kleiber,et al.  Numerical analysis of dynamic quasi-bifurcation , 1987 .

[4]  C. C. Rankin,et al.  Numerical aspects of shell stability analysis , 1990 .

[5]  G. Moore,et al.  The Calculation of Turning Points of Nonlinear Equations , 1980 .

[6]  H. Schwarz.  The eigenvalue problem (A − λB)x = 0 for symmetric matrices of high order , 1974 .

[7]  E. Riks.  The Application of Newton's Method to the Problem of Elastic Stability , 1972 .

[8]  Eugenio Oñate,et al.  Computational Mechanics of Nonlinear Response of Shells , 1990 .

[9]  Dov Shilkrut,et al.  Investigations of axisymmetric deformation of geometrically nonlinear, rotationally orthotropic, circular plates , 1983 .

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

[11]  M. Crisfield.  A FAST INCREMENTAL/ITERATIVE SOLUTION PROCEDURE THAT HANDLES "SNAP-THROUGH" , 1981 .

[12]  N. Akkas,et al.  Axisymmetric dynamic buckling of clamped shallow spherical and conical shells under step loads , 1970 .

[13]  R. S. Alwar,et al.  Axisymmetrie Dynamic Buckling of Shallow Spherical Shells , 1980 .

[14]  J. Altenbach.  Zienkiewicz, O. C., The Finite Element Method. 3. Edition. London. McGraw‐Hill Book Company (UK) Limited. 1977. XV, 787 S. , 1980 .

[15]  Ekkehard Ramm,et al.  Strategies for Tracing the Nonlinear Response Near Limit Points , 1981 .

[16]  E. Ramm,et al.  Dynamic stability analysis of shell structures , 1990 .

[17]  George J. Simitses,et al.  Dynamic Stability of Suddenly Loaded Structures , 1989 .