Nonlinear Stability Analysis of Sandwich Wide Panels—Part II: Postbuckling Response

2018 ◽  
Vol 85 (8) ◽  
Author(s):  
Zhangxian Yuan ◽  
George A. Kardomateas
Keyword(s):  
Continuation Method ◽  
Weak Form ◽  
Arc Length ◽  
Nonlinear Stability Analysis ◽  
Governing Equations ◽  
Buckling Mode ◽  
The Core ◽  
Global Buckling ◽  
Post Buckling ◽  
Branch Switching

The nonlinear post-buckling response of sandwich panels based on the extended high-order sandwich panel theory (EHSAPT) is presented. The model includes the transverse compressibility, the axial rigidity, and the shear effect of the core. Both faces and core are considered undergoing large displacements with moderate rotations. Based on the nonlinear weak form governing equations, the post-buckling response is obtained by the arc-length continuation method together with the branch switching technique. Also, the post-buckling response with imperfections is studied. The numerical examples discuss the post-buckling response corresponding to global buckling and wrinkling. It is found that due to the interaction between faces and core, localized effects may be easily initiated by imperfections after the sandwich structure has buckled globally. Furthermore, this could destabilize the post-buckling response. The post-buckling response verifies the critical load and buckling mode given by the buckling analysis in part I. The axial rigidity of the core, although it is very small compared to that of the faces, has a significant effect on the post-buckling response.

Nonlinear Stability Analysis of Sandwich Wide Panels—Part I: Buckling Behavior

2018 ◽  
Vol 85 (8) ◽  
Author(s):  
Zhangxian Yuan ◽  
George A. Kardomateas
Keyword(s):  
Critical Load ◽  
Nonlinear Stability ◽  
Sandwich Panels ◽  
Weak Form ◽  
Nonlinear Static Analysis ◽  
Nonlinear Stability Analysis ◽  
Buckling Mode ◽  
The Core ◽  
Buckling Behavior ◽  
Global Buckling

This is a series of two papers in which the nonlinear stability behavior of sandwich panels is investigated. This part presents the buckling behavior and focuses on the critical load and the buckling mode. The buckling analysis is based on the extended high-order sandwich panel theory (EHSAPT) which takes transverse compressibility and axial rigidity of the core into account. It allows for the interaction between the faces and the core. The geometric nonlinearity, i.e., large displacement with moderate rotation, is considered in both faces and core. The weak form governing equations are derived based on the EHSAPT-based element. Detailed formulations and analysis procedures are provided. It presents a general approach for arbitrary buckling type without decoupling it into isolated global buckling and wrinkling. There are no additional assumptions made about the prebuckling state and buckling mode shape, which are commonly presumed in the literature. In addition, edge effects which are also commonly neglected are included. The prebuckling state is determined via a nonlinear static analysis. Solving an eigenvalue problem yields the critical load and the corresponding eigenvector gives the buckling mode. Sandwich panels with different lengths are studied as examples. Both global buckling and wrinkling are observed. It shows that the axial rigidity of the core has a pronounced effect on both the critical load and the buckling mode.

Thermal post-buckling of laminated and isotropic rectangular plates with fixed edges: Comparison of experimental and numerical results

2012 ◽  
Vol 226 (10) ◽  
pp. 2393-2401 ◽  
Author(s):  
Marco Amabili ◽  
Mohammad Reza Sareban Tajahmadi
Keyword(s):  
Deformation Theory ◽  
Laboratory Experiments ◽  
Continuation Method ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Numerical Results ◽  
Rectangular Plates ◽  
Arc Length ◽  
Thermal Changes ◽  
Post Buckling

Post-buckling behaviors of laminated composite and isotropic rectangular plates subjected to various thermal changes are studied. Geometric imperfections are taken into account since they play a fundamental role. The plate is modeled using a nonlinear, higher order shear deformation theory. Plates with clamped edges are considered. A pseudo-arc length continuation method is used to obtain numerical results. Laboratory experiments have been performed in order to compare to the numerical calculations.

The Behavior of Column during Constrained Buckling Process

2012 ◽  
Vol 166-169 ◽  
pp. 385-391
Author(s):  
Xiu Gen Wu ◽  
Bai Lin Zheng ◽  
Peng Fei He ◽  
Shu Guang Liu
Keyword(s):  
Load Capacity ◽  
Reaction Force ◽  
Governing Equations ◽  
Buckling Mode ◽  
Euler Buckling ◽  
Post Buckling ◽  
Contact Models ◽  
Side Walls ◽  
Lateral Displacements ◽  
Fixed End

The elastic Euler buckling of an inextensible column is confined in a plane, and subject to fixed end displacement, in the presence of rigid, frictionless side-walls which constrain overall lateral displacements. The whole deflection is divided into some typical columns because of the symmetry. The governing equations of constrained buckling mode and deflection about axial load are deduced, based on linearized differential equation of beam. Point and line contact models are introduced to describe the behavior of the column in constrained buckling process, including load capacity, buckling wave and reaction force. The analysis on the deflection of column is helpful to the research about possible post-buckling paths.

scholarly journals Buckling Behavior of Non-Retrofitted and FRP-Retrofitted Steel CHS T-Joints

2021 ◽  
Vol 11 (7) ◽  
pp. 3098
Author(s):  
Amin Yazdi ◽  
Maria Rashidi ◽  
Mohammad Alembagheri ◽  
Bijan Samali
Keyword(s):  
Compressive Loading ◽  
Local Buckling ◽  
Buckling Mode ◽  
T Joints ◽  
Hollow Section ◽  
Frp Composite ◽  
Buckling Behavior ◽  
Global Buckling ◽  
Post Buckling ◽  
Circular Hollow Section

This paper aims to investigate the buckling behavior of circular hollow section (CHS) T-joints in retrofitted and non-retrofitted states under axial brace compressive loading. For this purpose, two types of analysis are carried out. The first one is evaluating the critical buckling load in various tubular joints, and the other one is investigating the post-buckling behavior after each buckling mode. More than 180 CHS T-joints with various normalized geometric properties were numerically modeled in non-retrofitted state to compute their governing buckling mode, i.e., chord ovalization, brace local, or global buckling. Then three joints with different buckling modes were selected to be retrofitted by fiber-reinforced polymer (FRP) patches to illustrate the improving effect of the FRP wrapping on the post-buckling performance of the retrofitted joints. In addition, FRP composite failures were investigated. The results indicate that the FRP retrofitting is able to prevent the brace local buckling, and that matrix failure is the most common composite failure in the retrofitted joints.

An Experimental on Honeycomb Core in the Axial Direction under the Quasi-Static Loading

2014 ◽  
Vol 699 ◽  
pp. 405-410
Author(s):  
Alif Zulfakar bin Pokaad ◽  
Md Radzai bin Said ◽  
Fauzi bin Ahmad ◽  
Mohd Nazeri bin Kamaruddin
Keyword(s):  
Elastic Characteristic ◽  
Axial Direction ◽  
Static Response ◽  
Honeycomb Core ◽  
Buckling Mode ◽  
Linear Elastic ◽  
The Core ◽  
Out Of Plane ◽  
Global Buckling ◽  
Aluminum Honeycomb

This paper focuses on the quasi-static response of the aluminum honeycomb core based on an experimental work. The load-compression and energy absorb characteristics of the out-of-plane aluminium honeycomb core are studied for three varieties of the core cell sizes which are 0.01905, 0.0127 and 0.00635 m. The crushing tests were conducted on the Instron machine with a displacement control of 5 mm/min. The initial part in the load-displacement graph shows linear elastic characteristic, followed by a non-linear elastic-plastic regime before it collapses. Based on the observation, the cell sized 0.01905 m shows the global buckling collapse, but the cell sized 0.0127 and 0.00635 m collapse as progressive buckling mode. The cell size 0.00635 m shows highest energy absorption due to it has the highest density and it collapses like the progressive buckling mode compared with the others specimen.

scholarly journals A New Analytical Approach for Nonlinear Global Buckling of Spiral Corrugated FG-CNTRC Cylindrical Shells Subjected to Radial Loads

2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Global Buckling ◽  
Homogenization Model ◽  
Corrugated Structure ◽  
The Galerkin Method

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.

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

A numerical approach based on finite element method for the wrinkling analysis of dielectric elastomer membranes

2021 ◽  
pp. 1-37
Author(s):  
Guoyong Mao ◽  
Wei Hong ◽  
Martin Kaltenbrunner ◽  
Shaoxing Qu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thickness Distribution ◽  
Numerical Approach ◽  
Dielectric Elastomer ◽  
Equivalent Model ◽  
Maxwell Stress ◽  
Buckling Mode ◽  
Post Buckling ◽  
Element Method

Abstract Dielectric elastomer (DE) actuators are deformable capacitors capable of a muscle-like actuation when charged. When subjected to voltage, DE membranes coated with compliant electrodes may form wrinkles due to the Maxwell stress. Here, we develop a numerical approach based on the finite element method (FEM) to predict the morphology of wrinkled DE membranes mounted on a rigid frame. The approach includes two steps, I) pre-buckling and II) post-buckling. In step I, the first buckling mode of the DE membrane is investigated by substituting the Maxwell stress with thermal stress in the built-in function of the FEM platform SIMULIA Abaqus. In step II, we use this first buckling mode as an artificial geometric imperfection to conduct the post-buckling analysis. For this purpose, we develop an equivalent model to simulate the mechanical behavior of DEs. Based on our approach, the thickness distribution and the thinnest site of the wrinkled DE membranes subjected to voltage are investigated. The simulations reveal that the crests/troughs of the wrinkles are the thinnest sites around the center of the membrane and corroborate these findings experimentally. Finally, we successfully predict the wrinkles of DE membranes mounted on an isosceles right triangle frame with various sizes of wrinkles generated simultaneously. These results shed light on the fundamental understanding of wrinkled dielectric elastomers but may also trigger new applications such as programmable wrinkles for optical devices or their prevention in DE actuators.

scholarly journals Disconnected stationary solutions for 3D Kolmogorov flow problem: preliminary results

2021 ◽  
Vol 2090 (1) ◽  
pp. 012046
Author(s):  
Nikolay M. Evstigneev
Keyword(s):  
Flow Problem ◽  
Stokes Equations ◽  
Continuation Method ◽  
Fourier Method ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
System Of Nonlinear Equations ◽  
Arc Length ◽  
Navier Stokes Equations ◽  
Numerical Bifurcation

Abstract The extension of the classical A.N. Kolmogorov’s flow problem for the stationary 3D Navier-Stokes equations on a stretched torus for velocity vector function is considered. A spectral Fourier method with the Leray projection is used to solve the problem numerically. The resulting system of nonlinear equations is used to perform numerical bifurcation analysis. The problem is analyzed by constructing solution curves in the parameter-phase space using previously developed deflated pseudo arc-length continuation method. Disconnected solutions from the main solution branch are found. These results are preliminary and shall be generalized elsewhere.

Meshless Integral Method for Analysis of Elastoplastic Geotechnical Materials

2010 ◽  
Author(s):  
Jianfeng Ma ◽  
Joshua David Summers ◽  
Paul F. Joseph
Keyword(s):  
Boundary Conditions ◽  
Function Approximation ◽  
Integral Method ◽  
Weak Form ◽  
Constitutive Law ◽  
Governing Equations ◽  
Natural Boundary ◽  
Pressure Sensitive ◽  
Support Domain ◽  
Natural Boundary Conditions

The meshless integral method based on regularized boundary equation [1][2] is extended to analyze elastoplastic geotechnical materials. In this formulation, the problem domain is clouded with a node set using automatic node generation. The sub-domain and the support domain related to each node are also generated automatically using algorithms developed for this purpose. The governing integral equation is obtained from the weak form of elastoplasticity over a local sub-domain and the moving least-squares approximation is employed for meshless function approximation. The geotechnical materials are described by pressure-sensitive multi-surface Drucker-Prager/Cap plasticity constitutive law with hardening. A generalized collocation method is used to impose the essential boundary conditions and natural boundary conditions are incorporated in the system governing equations. A comparison of the meshless results with the FEM results shows that the meshless integral method is accurate and robust enough to solve geotechnical materials.

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