Theoretical Analysis on Nonlinear Buckling, Post-buckling of Slender Beams and Bi-stable Mechanisms

2021 ◽  
pp. 1-14
Author(s):  
Ke Wu ◽  
Gang Zheng
Keyword(s):  
Compliant Mechanisms ◽  
Beam Theory ◽  
Stable States ◽  
Nonlinear Buckling ◽  
Theoretical Derivation ◽  
Deforma Tion ◽  
Theoretical Investigations ◽  
Slender Beams ◽  
Post Buckling ◽  
Kinematic Models

Abstract Compliant Mechanisms (CMs) are used to transfer motion, force and energy, taking advantages of the elastic deforma- tion of the involved compliant members. A branch of spe- cial type of elastic phenomenon called (post) buckling has been widely considered in CMs: avoiding buckling for better payload-bearing capacity and utilizing post-buckling to pro- duce multi-stable states. This paper digs into the essence of beam's bucking and post-bucking behaviors where we start from the famous Euler–Bernoulli beam theory and then ex- tend the mentioned linear theory into geometrically nonlin- ear one to handle multi-mode buckling problems via intro- ducing the concept of bifurcation theory. Five representative beam buckling cases are studied in this paper, followed by detailed theoretical investigations of their post-buckling be- haviors where the multi-state property has been proved. We finally propose a novel type of bi-stable mechanisms termed as Pre-buckled Bi-stable Mechanisms (PBMs) that integrate the features of both rigid and compliant mechanisms. The theoretical insights of PBMs are presented in detail for future studies. To the best of our knowledge, this paper is the first ever study on the theoretical derivation of the kinematic models of PBMs, which could be an important contribution to this field.

Programmable Multistable Mechanisms: Synthesis and Modeling

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Mohamed Zanaty ◽  
Ilan Vardi ◽  
Simon Henein
Keyword(s):  
Compliant Mechanisms ◽  
Reaction Force ◽  
Stable State ◽  
Beam Theory ◽  
Qualitative Behavior ◽  
Stable States ◽  
New Family ◽  
Fixed Constant ◽  
Numerical Finite Element ◽  
Euler Bernoulli Beam

Compliant mechanisms can be classified according to the number of their stable states and are called multistable mechanisms if they have more than one stable state. We introduce a new family of mechanisms for which the number of stable states is modified by programming inputs. We call such mechanisms programmable multistable mechanisms (PMM). A complete qualitative analysis of a PMM, the T-mechanism, is provided including a description of its multistability as a function of the programming inputs. We give an exhaustive set of diagrams illustrating equilibrium states and their stiffness as one programming input varies while the other is fixed. Constant force behavior is also characterized. Our results use polynomial expressions for the reaction force derived from Euler–Bernoulli beam theory. Qualitative behavior follows from the evaluation of the zeros of the polynomial and its discriminant. These analytical results are validated by numerical finite element method simulations.

Post-buckling inelastic analysis of thin-walled metal members using the Generalised Beam Theory

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Miguel Abambres
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Beam Theory ◽  
Flow Theory ◽  
Promising Alternative ◽  
Inelastic Analysis ◽  
Post Buckling ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalised Beam Theory

A 2nd order inelastic Generalised Beam Theory (GBT) formulation based on the J2 flow theory is proposed, being a promising alternative to the shell finite element method. Its application is illustrated for an I-section beam and a lipped-C column. GBT results were validated against ABAQUS, namely concerning equilibrium paths, deformed configurations, and displacement profiles. It was concluded that the GBT modal nature allows (i) precise results with only 22% of the number of dof required in ABAQUS, as well as (ii) the understanding (by means of modal participation diagrams) of the behavioral mechanics in any elastoplastic stage of member deformation .

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.

Nonlinear buckling and post-buckling analysis of imperfect porous plates under mechanical loads

2018 ◽  
Vol 22 (6) ◽  
pp. 1910-1930 ◽  
Author(s):  
Tran Minh Tu ◽  
Le Kha Hoa ◽  
Dang Xuan Hung ◽  
Le Thanh Hai
Keyword(s):  
Boundary Condition ◽  
Porous Plate ◽  
Nonlinear Buckling ◽  
Theoretical Formulation ◽  
Porosity Distribution ◽  
Buckling Behavior ◽  
Geometrical Imperfection ◽  
Porosity Coefficient ◽  
Post Buckling ◽  
Classical Shell Theory

The nonlinear buckling and post-buckling response of imperfect porous plates is investigated analytically in this paper. The porous materials with elastic moduli are assumed to vary through the thickness of the plate according to two different distribution types. Governing equations are derived based on the classical shell theory taking into account Von Karman nonlinearity and initial geometrical imperfection. Explicit relations of load–deflection curves for rectangular porous plates are determined by applying stress function and Galerkin’s method. The accuracy of present theoretical formulation is verified by comparing it with available results in the literature. The effects of varying porosity distribution, porosity coefficient, boundary condition and imperfection on post-buckling behavior of the porous plate are studied in detail. A parametric study is carried out to investigate the effects of varying porosity distribution, porosity coefficient, boundary condition and imperfection on post-buckling behavior of the porous plate. The results show that the critical buckling loads decrease with increasing porosity coefficient and the post-buckling curves for nonlinear symmetric porosity distribution are always higher than those for nonlinear non-symmetric porosity.

Effect of Matching Buckling Loads on Post-Buckling Behavior in Compliant Mechanisms

2021 ◽  
Author(s):  
A. Numić ◽  
T. W. A. Blad ◽  
F. van Keulen
Keyword(s):  
Compliant Mechanisms ◽  
Relative Length ◽  
Optimal Designs ◽  
Element Analysis ◽  
Buckling Loads ◽  
Actuation Force ◽  
Stepped Beam ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Novel Method

Abstract In this paper, a novel method for stiffness compensation in compliant mechanisms is investigated. This method involves tuning the ratio between the first two critical buckling loads. To this end, the relative length and width of flexures in two architectures, a stepped beam and parallel guidance, are adjusted. Using finite element analysis, it is shown that by maximizing this ratio, the actuation force for transversal deflection in post-buckling is reduced. These results were validated experimentally by identifying the optimal designs in a given space and capturing the force-deflection characteristics of these mechanisms.

Buckling and Post Buckling Behavior of a Transversely Stiffened Ship Hull Model

1964 ◽  
Vol 8 (04) ◽  
pp. 7-21
Author(s):  
H.G. Schultz
Keyword(s):  
Reasonable Agreement ◽  
Ship Hull ◽  
Buckling Load ◽  
Experimental Results ◽  
Postbuckling Behavior ◽  
Pure Bending ◽  
Box Girder ◽  
Buckling Behavior ◽  
Theoretical Investigations ◽  
Post Buckling

In the paper presented the behavior of a transversely formed box-girder model subjected to pure bending is discussed, where the deck plating of the model is loaded above the buckling load. The experimental results obtained are in reasonable agreement with theoretical investigations and show the influence of fabrication initiated plate deflections on the buckling and postbuckling behavior of the deck plating clearly. A method is suggested for determining the buckling load of plates having large initial deformations.

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