Abstract
An algorithm of physically and geometrically nonlinear static analysis of structures by the finite element method is described, the distinguishing feature of which is the use of a full nonlinear stiffness matrix. This matrix is represented as the sum of five terms, namely, the stiffness matrix of the zero, first and second order, as well as matrices of initial displacements and initial stresses. When using modified Lagrange coordinates, the matrix of the initial displacements becomes a zero matrix. The calculation is carried out by a step-by-step method. Features of the application of this technique in the calculation of reinforced concrete structures are considered. The examples of static nonlinear analysis of reinforced concrete structures with the aid of program PRINS are given.
Highlights
The reinforced concrete structures analysis with account of physical and geometrical nonlinearities by finite element method was released in many computer programs, such as NASTRAN [1], ANSYS [2], ABAQUS [3], ADINA [4], DIANA[5] and others
To illustrate the possibilities of the proposed methodology the load-bearing capacity for two structures was investigated with the aid of program PRINS
The investigations carried out in the present study have shown that the method of physically and geometrically nonlinear calculation realized in the PRINS program gives the opportunity to analyze in detail the processes of deformation of reinforced concrete trusses and slabs with both traditional reinforcement and reinforcement with composite fabrics
Summary
The reinforced concrete structures analysis with account of physical and geometrical nonlinearities by finite element method was released in many computer programs, such as NASTRAN [1], ANSYS [2], ABAQUS [3], ADINA [4], DIANA[5] and others. It’s obvious that Newton-Raphson method allows to reach the given tolerance for less number of iterations compared to modified Newton-Raphson, but it’s not obvious, that total time of solution will be less. In the computer finite element programs the BFGS (Broyden-Fletcher-Goldfarb-Shanno) method has found the greatest application (see, for example,[7])
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