Column calculation methods considering non-linear material behavior


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Title: Column calculation methods considering non-linear material behavior

Author(s): Ortega, M.A.; Romero, J.L.; de la Rosa Oliver, E.

Publication: ACHE

Volume: 57

Issue: 241

Appears on pages(s): 73 - 94


Date: 1/5/2006

This paper reviews methods for calculating columns with non-linear elastic materials as separate elements as a first step in the study of general structures formed compressed prismatic elements. First, an introduction is given, specifying the mechanical, kinematic and constitutive aspects used as a basis for outlining different types of column models. In this respect, we mention the models (Euler, Kirchhoff, Engesser, Shanley) which, from a historical viewpoint, have provided the central ideas (paths, stability, critical points) for understanding the behavior of columns. Second, the model is presented, as is the equation governing its behaviour, with respect to which a number classical equation-solving equation methods (the deflection, curvature and moment methods, and Newmark?s method) are mentioned. Also, the general rules for applying the method of finite elements for column calculation, as well as some of its more recent variations (linear elements) are specified. Third, two methods based on the theory of generalized splines and the concept of equivalent linear pillar are described [Ort04]: ? Algebraic method, which can be considered as an analytical method for solving common structures calculation problems and which is facilitated by the theory of generalized splines. ? General method, based on the joint use of the method of the finite elements and homothopy techniques to solve general non-linear problems of loads, materials and boundary conditions. Both methods are applied to column analysis with non-linear elastic material and are illustrated by means of examples that highlight their features.

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