On Post-Buckling Behavior of Edge Cracked Functionally Graded Beams Under Axial Loads

2015 ◽  
Vol 15 (04) ◽  
pp. 1450065 ◽  
Author(s):  
Şeref Doğuşcan Akbaş
Keyword(s):  
Nonlinear Problems ◽  
Functionally Graded ◽  
Element Approximation ◽  
Axial Loads ◽  
Buckling Behavior ◽  
Highly Nonlinear ◽  
Compressive Loads ◽  
Graded Material ◽  
Post Buckling ◽  
Fgm Beam

This paper presents the post-buckling analysis of an edge cracked cantilever beam composed of functionally graded material (FGM) subjected to axial compressive loads by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the height direction according to the exponential distribution. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. For beams subjected to compression loads, the load rise causes compressible forces and therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The highly nonlinear problem considered herein is solved incrementally by using the finite element method in conjunction with the Newton–Raphson method, by which the full geometric nonlinearity is considered. There is no restriction on the magnitudes of deflections and rotations in contradistinction to the von Karman strain displacement relations of the beam. In the study, the effects of the location and depth of the crack, and different material distributions on the post-buckling behavior of the FGM beam are investigated in detail.

Post-Buckling Analysis of Axially Functionally Graded Three-Dimensional Beams

2015 ◽  
Vol 07 (03) ◽  
pp. 1550047 ◽  
Author(s):  
Şeref Doğuşcan Akbaş
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Element Model ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Highly Nonlinear ◽  
Lagrangian Finite Element ◽  
Post Buckling

Post-buckling analysis of an axially functionally graded (AFG) cantilever beam subjected to an axial nonfollower compression load is studied in this paper by using the total Lagrangian finite element model of three-dimensional continuum approximations. Material properties of the beam change in the axial direction according to a power-law function. In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of three-dimensional continuum for an eight-node quadratic element. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton–Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations. The obtained results are compared with the published results. In this study, the effects of the material distribution on the post-buckling response of the AFG beam are investigated in detail. The differences between of material distributions are investigated in the post-buckling analysis. Numerical results show that the above-mentioned effects play a very important role on the post-buckling responses of the beam, and it is believed that new results are presented for post-buckling of AFG beams which are of interest to the scientific and engineering community in the area of FGM structures.

A study on non-linear post-buckling behavior of tapered Timoshenko beam made of functionally graded material under in-plane thermal loadings

2016 ◽  
Vol 52 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Amlan Paul ◽  
Debabrata Das
Keyword(s):  
Functionally Graded Material ◽  
Timoshenko Beam ◽  
Temperature Rise ◽  
Functionally Graded ◽  
Buckling Load ◽  
Uniform Temperature ◽  
Buckling Behavior ◽  
Non Linear ◽  
Graded Material ◽  
Post Buckling

In the present work, the non-linear post-buckling load–deflection behavior of tapered functionally graded material beam is studied for different in-plane thermal loadings. Two different thermal loadings are considered. The first one is due to the uniform temperature rise and the second one is due to the steady-state heat conduction across the beam thickness leading to non-uniform temperature rise. The governing equations are derived using the principle of minimum total potential energy employing Timoshenko beam theory. The solution is obtained by approximating the displacement fields following Ritz method. Geometric non-linearity for large post-buckling behavior is considered using von Kármán type non-linear strain-displacement relationship. Stainless steel/silicon nitride functionally graded material beam is considered with temperature-dependent material properties. The validation of the present work is successfully performed using finite element software ANSYS and using the available result in the literature. The post-buckling load–deflection behavior in non-dimensional plane is presented for different taperness parameters and also for different volume fraction indices. Normalized transverse deflection fields are presented showing the shift of the point of maximum deflection for various deflection levels. The results are new of its kind and establish benchmark for studying non-linear thermo-mechanical behavior of tapered functionally graded material beam.

Effects of pores on nonlinear vibration and post buckling behavior of functionally graded material pipes conveying fluid

2021 ◽  
pp. 095440622098201
Author(s):  
Nan Li ◽  
Hongyan Zhang ◽  
Changqing Bai
Keyword(s):  
Dynamic Behavior ◽  
Functionally Graded Material ◽  
Primary Resonance ◽  
Functionally Graded ◽  
Pore Distribution ◽  
Buckling Behavior ◽  
Graded Material ◽  
Post Buckling ◽  
Pipes Conveying Fluid ◽  
Conveying Fluid

Functionally graded material (FGM) has an important application prospect in aircraft engineering, especially in smart aircraft. The dynamic behavior of FGM has been widely investigated so far but more work is needed for the porous FGM pipes conveying fluid. In this paper, a sensible pore distribution function related with the volume fraction of metal and ceramic is proposed for the dynamic modeling of porous FGM pipes conveying fluid. The maximum porosity and its corresponding position are taken into account in the present mechanical model. The material properties of the porous pipes are temperature dependent and can be affected by pore distribution. The governing equation of the porous FGM pipe is derived and then the exact solution of post buckling is obtained. The nonlinear primary resonance is determined by the multiple scale method. It is shown that the effect of the pore distribution is very significant on the post buckling behavior and nonlinear primary resonance of the porous FGM pipes. The current work is very helpful in understanding the influence of pore distribution on static and dynamic behavior of pores FGM structures in engineering practice.

Nonlinear Stability of Sandwich Functionally Graded Cylindrical Shells with Stiffeners Under Axial Compression in Thermal Environment

2019 ◽  
Vol 19 (07) ◽  
pp. 1950073 ◽  
Author(s):  
Nguyen Thi Phuong ◽  
Vu Hoai Nam ◽  
Nguyen Thoi Trung ◽  
Vu Minh Duc ◽  
Pham Van Phong
Keyword(s):  
Thermal Stresses ◽  
Thermal Environment ◽  
Cylindrical Shells ◽  
Geometrical Nonlinearity ◽  
Functionally Graded ◽  
Nonlinear Buckling ◽  
Buckling Behavior ◽  
Compressive Loads ◽  
Graded Material ◽  
Orthogonal Stiffeners

The geometrically nonlinear response of sandwich functionally graded cylindrical shells reinforced by orthogonal and/or spiral stiffeners and subjected to axial compressive loads is investigated in this paper. Two types of sandwich functionally graded material models are considered. The formulations are based on the Donnell shell theory considering geometrical nonlinearity and Pasternak’s elastic foundation. The improved Lekhnitskii’s smeared stiffener technique is used to account for the stiffener effects with both mechanical and thermal stresses. The results obtained indicate that the spiral stiffeners have significantly beneficial influences in comparison with orthogonal stiffeners on the nonlinear buckling behavior of shells. The relatively large effects of temperature change, geometrical and material parameters are also demonstrated in the numerical investigations.

Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners

2019 ◽  
Vol 233 (17) ◽  
pp. 6177-6196 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dang Thuy Dong ◽  
Nguyen Thoi Trung ◽  
Nguyen Van Tue
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Thermal Environment ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Deformation Plate Theory ◽  
Graded Material ◽  
Post Buckling

In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

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