General P-Δ Method in Discrete Optimization of Frames

  • Andrew T. Janczura
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


The general P-Δ approach (GAPN) for the finite element method (FEM) in discrete optimization of frames has been presented in this paper.

It has been shown that P-Δ effects and suitable solutions algorithms comes from some modifications of the standard secant stiffness method for the second order theory (MNII) in general.

The GΔPN method is accurate approximation of the MNII with opposite to a standard (SΔP) and a modified (MΔP) P-Δ methods. Moreover SΔP and MΔP methods are use to be applied to the rectangular frame. vith oposite to the GΔPN.

The GΔPN approach is highly recomended for discrete optimization models of frames because is much effective as fastest in computer time, enough accurate and convergent even in critical area then the MNIIN.

With respect to structures, especially rectangular frames,the GΔPN method, its first linearization (GΔPL), standard and modified P-A methods, full nonlinear MNII and its linearization NMIIL has been compared.

One representative example of the frame has been chosen. A behaviour of GΔP methods in noncritical and critical area of loading with respect to their convergence has been considered.

A numerical example shows that all P-delta methods with comparison to the exact second order analysis gives satisfied results in noncritical area but received by the GAP methods are the best. Moreover from the P-Δ approaches, only the general P-A is convergent in a critical area of loading.


Critical Area Discrete Optimization Torsional Moment Rectangular Frame Joint Number 
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© Springer-Verlag, Berlin Heidelberg 1994

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  • Andrew T. Janczura

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