In-Plane Nonlinear Buckling of Funicular Arches

2015 ◽  
Vol 15 (05) ◽  
pp. 1450073 ◽  
Author(s):  
Jianbei Zhu ◽  
Mario M. Attard ◽  
David C. Kellermann
Keyword(s):  
Numerical Technique ◽  
Constitutive Relations ◽  
Finite Strains ◽  
Equilibrium Path ◽  
Shear Rigidity ◽  
Equilibrium Equations ◽  
Buckling Mode ◽  
Nonlinear Buckling ◽  
Shear Component ◽  
Longitudinal Stretch

This paper presents a numerical technique to determine the full pre-buckling and post-buckling equilibrium path for elastic funicular arches. The formulation includes the effects of shear deformations and geometric nonlinearity due to large deformations. The Timoshenko beam hypothesis is adopted for incorporating shear. Finite strains are considered without approximation. The finite strains are defined in terms of the normal and shear component of the longitudinal stretch. The constitutive relations for the internal actions are based on a hyperelastic constitutive model. Using the differential equilibrium equations and the constitutive laws, the nonlinear buckling behavior of some typical funicular arches are investigated using the trapezoid method with Richardson extrapolation enhancement. The results are validated by using the finite element package ANSYS and solutions available in the literature. Examples include parabolic arches under a uniformly distributed gravity load, a catenary under a distributed load along the arch and a catenary arch under an overburden load. Parametric studies are performed to identify the factors that influence the nonlinear buckling of funicular arches. The axial to shear rigidity ratio is shown to have a significant effect on the buckling load and the buckling mode shape.

scholarly journals Eigenproblem Versus the Load-Carrying Capacity of Hybrid Thin-Walled Columns with Open Cross-Sections in the Elastic Range

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3468
Author(s):  
Zbigniew Kolakowski ◽  
Andrzej Teter
Keyword(s):  
Cross Sections ◽  
Carrying Capacity ◽  
Ultimate Load ◽  
Equilibrium Path ◽  
Load Carrying Capacity ◽  
Nonlinear Buckling ◽  
Elastic Range ◽  
Load Carrying ◽  
Thin Walled ◽  
Ultimate Load Carrying Capacity

The phenomena that occur during compression of hybrid thin-walled columns with open cross-sections in the elastic range are discussed. Nonlinear buckling problems were solved within Koiter’s approximation theory. A multimodal approach was assumed to investigate an effect of symmetrical and anti-symmetrical buckling modes on the ultimate load-carrying capacity. Detailed simulations were carried out for freely supported columns with a C-section and a top-hat type section of medium lengths. The columns under analysis were made of two layers of isotropic materials characterized by various mechanical properties. The results attained were verified with the finite element method (FEM). The boundary conditions applied in the FEM allowed us to confirm the eigensolutions obtained within Koiter’s theory with very high accuracy. Nonlinear solutions comply within these two approaches for low and medium overloads. To trace the correctness of the solutions, the Riks algorithm, which allows for investigating unsteady paths, was used in the FEM. The results for the ultimate load-carrying capacity obtained within the FEM are higher than those attained with Koiter’s approximation method, but the leap takes place on the identical equilibrium path as the one determined from Koiter’s theory.

Buckling Mode Interaction in Composite Plate Assemblies

1995 ◽  
Vol 48 (11S) ◽  
pp. S52-S60 ◽  
Author(s):  
Ioannis G. Raftoyiannis ◽  
Luis A. Godoy ◽  
Ever J. Barbero
Keyword(s):  
Linear Elasticity ◽  
Composite Plate ◽  
Mode Interaction ◽  
Equilibrium Path ◽  
Buckling Mode ◽  
Fiber Reinforced Composite ◽  
Composite Columns ◽  
Reinforced Composite ◽  
Coupled Solution ◽  
Coordinate Basis

The analysis of buckling mode interaction of fiber-reinforced composite columns, modeled as plate assemblies, is presented. The main assumptions are linear elasticity; a linear fundamental equilibrium path; the existence of critical states that are coincident or near coincident; and a coupled path rising from a quadratic combination of modal displacements due to interaction. The formulation adopted is known as the W-formulation, in which the energy is written in terms of a sliding set of incremental coordinates, measured with respect to the fundamental path. The energy is then expressed with respect to a reduced modal coordinate basis, and the coupled solution arising from interaction is computed. An example of a pultruded composite I-column subjected to axial compression illustrates the procedure.

Instability of Discrete Pseudo-Conservative Structural Systems

1991 ◽  
Vol 44 (11S) ◽  
pp. S194-S198 ◽  
Author(s):  
Anibal E. Mirasso ◽  
Luis A. Godoy
Keyword(s):  
Classical System ◽  
Potential Energy Function ◽  
Structural Systems ◽  
Equilibrium Path ◽  
Equilibrium Equations ◽  
Total Potential ◽  
Approximate Form ◽  
Nonlinear Equilibrium ◽  
Mechanical Models ◽  
New Formulation

Critical and postcritical states of pseudo-conservative discrete structural systems are studied by means of a new formulation leading to a classification of critical states and to an approximate form of the postcritical equilibrium path. The nonlinear equilibrium equations are derived from the total potential energy function of a classical system, but with the addition of at least one control parameter. The follower force effect is thus included by nonlinear constraints to the equilibrium equation. The nonlinear equations are solved by perturbation techniques. Finally the theory is applied to investigate the instability of some simple mechanical models.

Analysis of Nonlinear Buckling of a Long-Span Elliptic Paraboloid Suspended Dome Structure

2013 ◽  
Vol 639-640 ◽  
pp. 191-197 ◽  
Author(s):  
Zheng Rong Jiang ◽  
Kai Rong Shi ◽  
Xiao Nan Gao ◽  
Qing Jun Chen
Keyword(s):  
Single Layer ◽  
Buckling Mode ◽  
Nonlinear Buckling ◽  
Elliptic Paraboloid ◽  
Geometric Imperfection ◽  
Long Span ◽  
Initial Geometric Imperfection ◽  
Dome Structure ◽  
Unsymmetrical Loading ◽  
The Stability

The suspended dome structure, which is a new kind of hybrid spatial one composed of the upper single layer latticed shell and the lower cable-strut system, generally has smaller rise-to-span ratio, thus the overall stability is one of the key factors to the design of the structure. The nonlinear buckling behavior of an elliptic paraboloid suspended dome structure of span 110m80m is investigated by introducing geometric nonlinearity, initial geometric imperfection, material elastic-plasticity and half-span distribution of live loads. The study shows that the coefficient of stable bearing capacity usually is not minimal when the initial geometric imperfection configuration is taken as the first order buckling mode. The unsymmetrical loading distribution and the material nonlinearity might have significant effects on the coefficient. The structure is sensitive to the changes of initial geometric imperfection, and the consistent mode imperfection method is not fully applicable to the stability analysis of suspended dome structure.

NONLINEAR GENERALIZED BEAM THEORY FOR COLD-FORMED STEEL MEMBERS

2003 ◽  
Vol 03 (04) ◽  
pp. 461-490 ◽  
Author(s):  
N. SILVESTRE ◽  
D. CAMOTIM
Keyword(s):  
Numerical Technique ◽  
Beam Theory ◽  
Equilibrium Equations ◽  
Steel Members ◽  
Mode Decomposition ◽  
Nonlinear Equilibrium ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
Cold Formed Steel ◽  
Generalized Beam Theory

A geometrically nonlinear Generalized Beam Theory (GBT) is formulated and its application leads to a system of equilibrium equations which are valid in the large deformation range but still retain and take advantage of the unique GBT mode decomposition feature. The proposed GBT formulation, for the elastic post-buckling analysis of isotropic thin-walled members, is able to handle various types of loading and arbitrary initial geometrical imperfections and, in particular, it can be used to perform "exact" or "approximate" (i.e., including only a few deformation modes) analyses. Concerning the solution of the system of GBT nonlinear equilibrium equations, the finite element method (FEM) constitutes the most efficient and versatile numerical technique and, thus, a beam FE is specifically developed for this purpose. The FEM implementation of the GBT post-buckling formulation is reported in some detail and then employed to obtain numerical results, which validate and illustrate the application and capabilities of the theory.

scholarly journals Multiscale analysis of instabilities in heterogeneous materials using ANM and multilevel FEM

2012 ◽  
Author(s):  
Saeid Nezamabadi ◽  
Hamid Zahrouni ◽  
Julien Yvonnet ◽  
Michel Potier-Ferry
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Multiscale Analysis ◽  
Numerical Technique ◽  
Constitutive Relations ◽  
Heterogeneous Materials ◽  
Perturbation Approach ◽  
Element Analysis ◽  
Numerical Examples ◽  
Asymptotic Numerical Method

In this study, we propose a numerical technique which combines a perturbation approach (asymptotic numerical method) and a multilevel finite element analysis. This procedure allows dealing with instability phenomena in the context of heterogeneous materials where buckling may occur at both macroscopic and/or microscopic scales. Different constitutive relations are applied and geometrical non-linearity is taken into account at both scales. Numerical examples involving instabilities at both micro and macro levels are presented.

scholarly journals Influence of geometrical imperfection on critical temperature evaluation for steel corrugated arch sheets exposed to fire

2019 ◽  
Vol 262 ◽  
pp. 09007
Author(s):  
Mariusz Maślak ◽  
Michał Pazdanowski ◽  
Maciej Suchodoła
Keyword(s):  
Critical Temperature ◽  
Steel Sheet ◽  
Local Buckling ◽  
Equilibrium Path ◽  
Buckling Mode ◽  
Initial Shape ◽  
Steel Sheets ◽  
Computational Environment ◽  
Geometrical Imperfection ◽  
Predetermined Level

The critical temperature for an arched corrugated steel sheet exposed to fully developed fire is determined in this paper. The analysis is performed on 3D numerical model developed within the ANSYS computational environment with parameters calibrated experimentally on an experiment performed for persistent design scenario. During the simulations performed the self-supporting steel sheet with an assumed initial shape imperfection is at first loaded with static load, up to a predetermined level of material effort, and subsequently evenly heated until the capability to safely resist the applied load is completely exhausted. Because of the nonlinearity of the analysis having several sources, the location of the limit point on the equilibrium path determined during calculations represents the temperature sought. Three imperfection patterns, denoted as A, B and C are considered. In the case A the imperfection has the shape and magnitude measured in situ, selected as representative for a set of 10 steel sheets of the same type. In the case B the imperfection is a substitute one with size analogous to that assumed in the case A, but with a different shape, corresponding to the first antisymmetric buckling mode identified in conventional Local Buckling Analysis (LBA). In the case C the shape of imperfection B has been kept, but the positive and negative deviation from the perfect circular shape have been increased twofold.

Effects of symmetric imperfections on the behavior of bistable struts

2016 ◽  
Vol 22 (12) ◽  
pp. 2240-2252 ◽  
Author(s):  
Jianguo Cai ◽  
Xiaowei Deng ◽  
Jian Feng
Keyword(s):  
Virtual Work ◽  
Variable Geometry ◽  
Equilibrium Equations ◽  
Buckling Mode ◽  
Concentrated Load ◽  
Virtual Work Principle ◽  
Shallow Arches ◽  
Buckling Behavior ◽  
Nonlinear Equilibrium ◽  
Post Buckling

The behavior of a bistable strut for variable geometry structures was investigated in this paper. A three-hinged arch subjected to a central concentrated load was used to study the effect of symmetric imperfections on the behavior of the bistable strut. Based on a nonlinear strain–displacement relationship, the virtual work principle was adopted to establish both the pre-buckling and buckling nonlinear equilibrium equations for the symmetric snap-through buckling mode. Then the critical load for symmetric snap-through buckling was obtained. The results show that the axial force is in compression before the arch is buckled, but it becomes in tension after buckling. Thus, the previous formulas cannot be used for the analysis of post-buckling behavior of three-hinged shallow arches. Then, the principle of virtual work was also used to establish the post-buckling equilibrium equations of the arch in the horizontal and vertical directions as well as the static boundary conditions, which are very important for bistable struts.

Sign in / Sign up

Export Citation Format

Share Document