A computational algorithm, based on the combined use of mixed finite elements and classical Rayleigh–Ritz approximation, is presented for predicting the nonlinear static response of structures; The fundamental unknowns consist of nodal displacements and forces (or stresses) and the governing nonlinear finite element equations consist of both the constitutive relations and equilibrium equations of the discretized structure. The vector of nodal displacements and forces (or stresses) is expressed as a linear combination of a small number of global approximation functions (or basis vectors), and a Rayleigh–Ritz technique is used to approximate the finite element equations by a reduced system of nonlinear equations. The global approximation functions (or basis vectors) are chosen to be those commonly used in static perturbation technique; namely a nonlinear solution and a number of its path derivatives. These global functions are generated by using the finite element equations of the discretized structure.
The potential of the global–local mixed approach and its advantages over global–local displacement finite element methods are discussed. Also, the high accuracy and effectiveness of the proposed approach are demonstrated by means of numerical examples.
[1]
P. Bergan,et al.
Solution techniques for non−linear finite element problems
,
1978
.
[2]
G. Dhatt,et al.
Finite element large deflection analysis of shallow shells
,
1976
.
[3]
Ahmed K. Noor,et al.
Reduced Basis Technique for Nonlinear Analysis of Structures
,
1980
.
[4]
Ahmed K. Noor,et al.
Nonlinear shell analysis via mixed isoparametric elements
,
1977
.
[5]
J. F. Besseling.
Non-linear analysis of structures by the finite element method as a supplement to a linear analysis
,
1974
.
[6]
Dennis A. Nagy,et al.
Modal representation of geometrically nonlinear behavior by the finite element method
,
1979
.
[7]
Ahmed K. Noor,et al.
Nonlinear finite element analysis of curved beams
,
1977
.
[8]
P. Stern,et al.
Automatic choice of global shape functions in structural analysis
,
1978
.
[9]
Graham H. Powell,et al.
Finite element analysis of non-linear static and dynamic response
,
1977
.