LARGE DISPLACEMENT BEAM MODEL FOR CREEP BUCKLING ANALYSIS OF FRAMED STRUCTURES

2009 ◽  
Vol 09 (01) ◽  
pp. 61-83 ◽  
Author(s):  
GORAN TURKALJ ◽  
DOMAGOJ LANC ◽  
JOSIP BRNIC
Keyword(s):  
Virtual Work ◽  
Buckling Analysis ◽  
Large Displacement ◽  
Isotropic Hardening ◽  
Beam Model ◽  
Inelastic Behavior ◽  
Equilibrium Equations ◽  
Virtual Work Principle ◽  
Framed Structures ◽  
Spatial Beam

In this work, a one-dimensional beam model for buckling analysis of framed structures under large displacement creep regimes is presented. The equilibrium equations of a prismatic and straight spatial beam element are formulated in the framework of corotational description, using the virtual work principle. Although the translations and rotations of the element are allowed to be large, the strains are assumed to be small. The material of a framed structure is assumed to be homogenous and isotropic. The bilinear elastic–plastic model with isotropic hardening and the power creep law are adopted for describing the inelastic behavior of the material. The numerical algorithm is implemented in a computer program called BMCA and its reliability is validated through test examples.

scholarly journals Design of a Monolithic Double-Slider Based Compliant Gripper with Large Displacement and Anti-Buckling Ability

Micromachines ◽  
2019 ◽  
Vol 10 (10) ◽  
pp. 665 ◽  
Author(s):  
Hao ◽  
Zhu
Keyword(s):  
Virtual Work ◽  
Large Displacement ◽  
Amplification Coefficient ◽  
Element Analysis ◽  
Virtual Work Principle ◽  
Manipulation System ◽  
The Finite Element Analysis ◽  
Rigid Body Model ◽  
Analytical Relations ◽  
Kinematic Mechanism

In a micro-manipulation system, the compliant gripper is used for gripping, handling and assembling of objects. Large displacement and anti-buckling characteristics are desired in the design of the gripper. In this paper, a compliant gripper with these two characteristics is proposed, modelled and verified. The large displacement is enabled by using distributed compliance in a double-slider kinematic mechanism. An inverted flexure arrangement enables the anti-buckling of the gripper when closing the two jaws. A pseudo-rigid-body model (PRBM) method with the help of virtual work principle is employed to obtain several desired analytical relations including the amplification coefficient and kinetostatics. The results of the finite element analysis (FEA) are shown to be consistent with the results of the derived analytical model. An experimental test was carried out through a milling machined aluminium alloy prototype, the results of which verify the good performance of the compliant gripper.

scholarly journals THIN ELASTIC PLATES EXPERIENCING LARGE DEFLECTIONS ABOVE THE VON KARMAN LIMITS

2021 ◽  
Author(s):  
Sergey Selyugin
Keyword(s):  
Virtual Work ◽  
Plate Thickness ◽  
Geometrically Nonlinear ◽  
Large Deflections ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Virtual Work Principle ◽  
Von Karman ◽  
Von Kármán ◽  
Thin Elastic Plates

Thin elastic plates (homogeneous or composite) experiencing large deflections are considered. The deflections are much larger than the plate thickness. The geometrically nonlinear elasticity theory and the Kirchhoff assumptions are employed. Small elongations and shears are assumed. Following Novozhilov, the strain expressions are derived. Then, under a small in-plane rotation assumption and using the virtual work principle, the equilibrium equations and the boundary conditions are obtained. The equations/conditions become the known von Karman ones for the case of moderate deflections. The solutions of the obtained equations may be used as benchmarks for the nonlinear structural analysis (e.g., FEM) software in the case of large deflections.

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.

scholarly journals Beam element for large displacement analysis of elasto-plastic frames

2004 ◽  
Vol 26 (1) ◽  
pp. 39-54
Author(s):  
Nguyen Dinh Kien ◽  
Do Quoc Quang
Keyword(s):  
Virtual Work ◽  
Internal Force ◽  
Beam Element ◽  
Large Displacement ◽  
Isotropic Hardening ◽  
Arc Length ◽  
Tangent Stiffness Matrix ◽  
Strain Relationship ◽  
Internal Force Vector ◽  
Finite Element Formulations

The present paper develops a non-linear beam element for analysis of elastoplastic frames under large displacements. The finite element formulations are derived by using the co-rotational approach and expression of the virtual work. The Gauss quadrature is employed for numerically computing the element tangent stiffness matrix and internal force vector. A bilinear stress-strain relationship with isotropic hardening is adopted to update the stress. The arc-length technique based on the Newton-Raphson iterative method is employed to compute the equilibrium paths. A number of numerical examples is employed to assess the performance of the developed element. The effects of plastic action on the large displacement behavior of the structures as well as the expansion of plastic zones in the loading process are discussed.

scholarly journals Funicularity in elastic domes: Coupled effects of shape and thickness

2021 ◽  
Vol 8 (1) ◽  
pp. 181-187
Author(s):  
Federico Accornero ◽  
Alberto Carpinteri
Keyword(s):  
Virtual Work ◽  
Static Problem ◽  
The Other ◽  
Curved Beams ◽  
Shells Of Revolution ◽  
Equilibrium Equations ◽  
Virtual Work Principle ◽  
Other Hand ◽  
Definition Of ◽  
Two Parameters

Abstract An historical overview is presented concerning the theory of shell structures and thin domes. Early conjectures proposed, among others, by French, German, and Russian Authors are discussed. Static and kinematic matrix operator equations are formulated explicitly in the case of shells of revolution and thin domes. It is realized how the static and kinematic matrix operators are one the ad-joint of the other, and, on the other hand, it can be rigorously demonstrated through the definition of stiffness matrix and the application of virtual work principle. In this context, any possible omission present in the previous approaches becomes evident. As regards thin shells of revolution (thin domes), the elastic problem results to be internally statically-determinate, in analogy to the case of curved beams, being characterized by a system of two equilibrium equations in two unknowns. Thus, the elastic solution can be obtained just based on the equilibrium equations and independently of the shape of the membrane itself. The same cannot be affirmed for the unidimensional elements without ‚exural stiffness (ropes). Generally speaking, the static problem of elastic domes is governed by two parameters, the constraint reactions being assumed to be tangential to meridians at the dome edges: the shallowness ratio and the thickness of the dome. On the other hand, when the dome thickness tends to zero, the funicularity emerges and prevails, independently of the shallowness ratio or the shape of the dome. When the thickness is finite, an optimal shape is demonstrated to exist, which minimizes the flexural regime if compared to the membrane one.

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

A PD Computed Torque Control Method with Online Self-gain Tuning for a 3UPS-PS Parallel Robot

Robotica ◽  
2021 ◽  
pp. 1-13
Author(s):  
Xiaogang Song ◽  
Yongjie Zhao ◽  
Chengwei Chen ◽  
Liang’an Zhang ◽  
Xinjian Lu
Keyword(s):  
Feedback Loop ◽  
Control Method ◽  
Virtual Work ◽  
Parallel Robot ◽  
Torque Control ◽  
Virtual Work Principle ◽  
Tuning Method ◽  
Computed Torque Control ◽  
Control Feedback ◽  
Computed Torque

SUMMARY In this paper, an online self-gain tuning method of a PD computed torque control (CTC) is used for a 3UPS-PS parallel robot. The CTC is applied to the 3UPS-PS parallel robot based on the robot dynamic model which is established via a virtual work principle. The control system of the robot comprises a nonlinear feed-forward loop and a PD control feedback loop. To implement real-time online self-gain tuning, an adjustment method based on the genetic algorithm (GA) is proposed. Compared with the traditional CTC, the simulation results indicate that the control algorithm proposed in this study can not only enhance the anti-interference ability of the system but also improve the trajectory tracking speed and the accuracy of the 3UPS-PS parallel robot.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

scholarly journals Application of the virtual work principle to compute magnetic forces with a volume integral method

2013 ◽  
Vol 27 (3) ◽  
pp. 418-432 ◽  
Author(s):  
Anthony Carpentier ◽  
Nicolas Galopin ◽  
Olivier Chadebec ◽  
Gérard Meunier ◽  
Christophe Guérin
Keyword(s):  
Integral Method ◽  
Virtual Work ◽  
Volume Integral ◽  
Virtual Work Principle ◽  
Magnetic Forces
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