Nonlinear Analysis Of Frame Structures Research Articles

A Generalized Numerical Procedure for Nonlinear Analysis of Frames Exhibiting a Limit or a Bifurcation Point

A generalized numerical scheme for nonlinear analysis of framed structures is presented. The proposed numerical technique is aimed at improving the reliability and efficiency of a computer program for nonlinear analysis of structures exhibiting a limit or a bifurcation point. A simple and automatic energy method for the transformation of a bifurcation point to a limit point for the tracing of the realistic post-buckling path is also suggested. The combined numerical strategy proposed in this paper and recommended for general non-linear problems will greatly enhance the feasibility and user-friendliness of a nonlinear analysis computer program for general users.

Non-linear analysis of framed structures with axial constraints

In tracing the lateral load-displacement characteristics of tall framed structures loaded up to their ultimate load one has to consider the non-linear effects resulting from material properties and geometry. Applying the incremental load approach, the problem is locally linearized at the ‘cost’ of recalculating the stiffness for each load increment. As a result, accumulation of numerical errors can degrade the accuracy of results. Matrix condensation, transformation of coordinates, and constraints on the axial deformations are combined to reduce the number of unknowns. Moreover, by introducing axial constraints, the numerical problem of ill-conditioned matrices due to combining large axial stiffnesses with relatively small flexural and rotational stiffnesses can be avoided. The inelastic moment-curvature and axial force-deformation behavior of structural members are modeled by Ramberg-Osgood curves. Partial geometric non-linearity is included through P- Δ effect, which considers the influence of the deformed structure on the incremental stiffness. Previous work has shown the basic concepts of the axial constraints and is extended to the non-linear analysis. The theoretical development of the analysis procedure has been incorporated into a computer program. Several examples are given to demonstrate the influence of the constraint level on the accuracy and efficiency of the analysis.

Geometrically nonlinear analysis of elastic framed structures

The development of a method for the elastic nonlinear analysis of framed structures is presented. It is capable of providing solutions up to and including any existing limit point. The effects of both member and structure deformations are accounted for. The solution strategy proposed rests on a judicious combination of the well-known Newton-Raphson iterative scheme and a novel modification of the arc-length method within a finite element based partially updated Lagrangian description. The proposed variation of the arc-length technique enables a solution at the limit point to be calculated. Very accurate results can be obtained as demonstrated by three examples, all solved using the computer program developed.

Interactive microcomputer programs for linear and non-linear static analysis of frameworks

The paper describes interactive microcomputer programs for linear and non-linear analysis of framed structures under static loading. These programs represent useful analytical complements to the design process used in structural engineering practice. The programs permit linear elastic analysis of two and three dimensional framed structures. The programs may be used in a sequential manner to predict the elastic instability loads of planar frames. They may also be used iteratively to model elastic-plastic behaviour of planar frames up to the simple plastic collapse condition. The paper highlights the value of structured programming in achieving memory conservation in microcomputers.

Nonlinear analysis of framed structures with a plasticity minded beam element

A general method for geometrical and material nonlinear analysis of planar framed structures is presented. The theoretical prerequisites prior to the development of a displacement type approach for a beam element in plasticity are established. The shape functions and stiffness matrix for a nined.o.f. beam element are evaluated. The generalised updated Lagrangian formulation is used to describe the equations of equilibrium and the predictions of a computer program are compared with examples ranging from buckling and elastica problems to experimental plasticity in steel and in reinforced concrete.

Finite Element Analysis of Buckling and Large Deflection Problems of Beam-Columns by using the Lower Oder Element Shape Functions

A new discrete method of analysis proposed by one of the author is found to be mathematically equivalent to the finite element analysis based on the lower order element shape functions.Standing on such viewpoint, use of beam elements with linear shape functions was attempted in finite element analysis of buckling and post-buckling characteristics of beam-columns in this paper.Results of numerical analyses duly showed validty of the proposed method in nonline aranalysis of framed structures with considerable reduction of computing time to compare with the existing method.

Elastic-Plastic Analysis of Framed Structures using the Matrix Method (3 rd Report)

Many types of framed structures are constructed of deep girders as the main supporting members. These girders are usually composed of deep webs. When such structures are subjected to external loads, local failures, such as buckling of webs or flanges, local yielding of a section or a part of a section etc...., are liable to occur. However, it is often experienced that structures can still carry further loads after local failures have occured.In the design of such structures, it is important to get information on the complete behaviour of the structure until final collapse, including the ultimate strength of the structure and the deformations of the members accompanied by different loading conditions.In this paper the load-deformation relationship before and after local failures (such as buckling and/or plastification) is investigated for a deep girder element subjected to a combined load of shearing force and bending moment. An analytical method for evaluating the ultimate strength of statically indeterminate structures consisting of deep girders is presented. This method is based on the matrix method for nonlinear analysis of framed structures, which was developed in the 1 st. and 2 nd. Reports of this series.Examples of analysis are performed on straight deep girders which are fixed at both ends. The results of analyses suggest that the ultimate strength analysis by the new method is important since the plastic analysis predicts sometimes much higher collapse load than that by the method which accounts for the effects of buckling. On the other hand, the elastic analysis estimates the carrying capacity much lower than the actual.