scholarly journals Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Diagnostyka ◽  
2021 ◽  
Vol 22 (1) ◽  
pp. 101-112
Author(s):  
Mohcine Chajdi ◽  
Adri Ahmed ◽  
Khalid El Bikri ◽  
Rhali Benamar
Keyword(s):  
Forced Vibrations ◽  
Functionally Graded ◽  
Stress Distributions ◽  
Cracked Beams

scholarly journals Stiffness Estimation of Cracked Beams Based on Nonlinear Stress Distributions Near the Crack

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Chunyu Fu ◽  
Yuyang Wang ◽  
Dawei Tong
Keyword(s):  
Crack Depth ◽  
Internal Force ◽  
Stress Distributions ◽  
Cracked Beam ◽  
Section Shape ◽  
Nonlinear Stress ◽  
Crack Depth Ratio ◽  
Element Technique ◽  
Force Equilibrium ◽  
Cracked Beams

The crack presence causes nonlinear stress distributions along the sections of a beam, which change the neutral axis of the sections and further affect the beam stiffness. Thus, this paper presents a method for the stiffness estimation of cracked beams based on the stress distributions. First, regions whose stresses are affected by the crack are analyzed, and according to the distance to the crack, different nonlinear stress distributions are modeled for the effect regions. The inertia moments of section are evaluated by substituting these stress distributions into the internal force equilibrium of section. Then the finite-element technique is adopted to estimate the stiffness of the cracked beam. The estimated stiffness is used to predict the displacements of simply supported beams with a crack, and the results show that both static and vibrational displacements are accurately predicted, which indicates that the estimated stiffness is precise enough. Besides, as the section shape of beam is not limited in the process of modeling the stress distributions, the method could be applicable not only to the stiffness estimation of cracked beams with a rectangular section, but also to that of the beams with a T-shaped section if the crack depth ratio is not larger than 0.7.

Thermal stress analysis of in-plane two-directional functionally graded plates subjected to in-plane edge heat fluxes

2016 ◽  
Vol 232 (8) ◽  
pp. 693-716
Author(s):  
MK Apalak ◽  
MD Demirbas
Keyword(s):  
Mechanical Properties ◽  
Thermal Stress ◽  
Functionally Graded ◽  
Heat Fluxes ◽  
Material Composition ◽  
Stress Distributions ◽  
Thermal And Mechanical Properties ◽  
Functionally Graded Plates ◽  
Spatial Derivatives ◽  
Derivatives Of

This study investigates the thermal stress and deformation states of bi-directional functionally graded clamped plates subjected to constant in-plane heat fluxes along two ceramic edges. The material properties of the functionally graded plates were assumed to vary with a power law along two in-plane directions not through the plate thickness direction. The spatial derivatives of thermal and mechanical properties of the material composition were considered, and the effects of the bi-directional composition variations and spatial derivative terms on the displacement, strain and stress distributions were also investigated. The heat conduction and Navier equations describing the two-dimensional thermo-elastic problem were discretized using finite-difference method, and the set of linear equations were solved using the pseudo singular value method. The compositional gradient exponents and the spatial derivatives of thermal and mechanical properties of the material composition were observed to play an important role especially on the heat transfer durations, the displacement and strain distributions, but had a minor effect on the temperature and stress distributions.

Vibrational behavior of sandwich plates with functionally graded wavy carbon nanotube-reinforced face sheets resting on Pasternak elastic foundation

2017 ◽  
Vol 24 (11) ◽  
pp. 2327-2343 ◽  
Author(s):  
Rasool Moradi-Dastjerdi ◽  
Hamed Momeni-Khabisi
Keyword(s):  
Carbon Nanotube ◽  
Aspect Ratio ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Forced Vibrations ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Free And Forced Vibrations ◽  
Mesh Free ◽  
Pasternak Elastic Foundation

In this paper, free and forced vibrations, and also resonance and pulse phenomena in sandwich plates with an isotropic core and composite reinforced by wavy carbon nanotube (CNT) face sheets are studied based on a mesh-free method and first order shear deformation theory (FSDT). The sandwich plates are resting on Pasternak elastic foundation and subjected to periodic loads. In the mesh-free analysis, moving least squares (MLS) shape functions are used for approximation of displacement field in the weak form of motion equation and the transformation method is used for imposition of essential boundary conditions. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak’s elastic foundation coefficients, sandwich plate thickness, face sheets thickness, plate aspect ratio and time depended force are investigated on the free and forced vibrations, and resonance behavior of the sandwich plates with wavy CNT-reinforced face sheets.

scholarly journals A Novel MDD-Based BEM Model for Transient 3T Nonlinear Thermal Stresses in FGA Smart Structures

2020 ◽  
Author(s):  
Mohamed Abdelsabour Fahmy
Keyword(s):  
Thermal Stress ◽  
Boundary Element ◽  
Thermal Stresses ◽  
Smart Structures ◽  
Industrial Applications ◽  
Functionally Graded ◽  
Numerical Results ◽  
Stress Distributions ◽  
Proposed Model ◽  
Further Development

The main objective of this chapter is to introduce a novel memory-dependent derivative (MDD) model based on the boundary element method (BEM) for solving transient three-temperature (3T) nonlinear thermal stress problems in functionally graded anisotropic (FGA) smart structures. The governing equations of the considered study are nonlinear and very difficult if not impossible to solve analytically. Therefore, we develop a new boundary element scheme for solving such equations. The numerical results are presented highlighting the effects of the MDD on the temperatures and nonlinear thermal stress distributions and also the effect of anisotropy on the nonlinear thermal stress distributions in FGA smart structures. The numerical results also verify the validity and accuracy of the proposed methodology. The computing performance of the proposed model has been performed using communication-avoiding Arnoldi procedure. We can conclude that the results of this chapter contribute to increase our understanding on the FGA smart structures. Consequently, the results also contribute to the further development of technological and industrial applications of FGA smart structures of various characteristics.

scholarly journals Experimental Investigation of Stress Distributions in 3D Printed Graded Plates with a Circular Hole

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7845
Author(s):  
Quanquan Yang ◽  
He Cao ◽  
Youcheng Tang ◽  
Yun Li ◽  
Xiaogang Chen
Keyword(s):  
Experimental Investigation ◽  
Stress Concentration ◽  
Young’S Modulus ◽  
Circular Hole ◽  
Young's Modulus ◽  
Theoretical Models ◽  
Research Field ◽  
Functionally Graded ◽  
Stress Distributions ◽  
Functionally Graded Plates

An experimental investigation is presented for the stress distributions in functionally graded plates containing a circular hole. On the basis of the authors’ previously constructed theoretical model, two kinds of graded plates made of discrete rings with increasing or decreasing Young’s modulus were designed and fabricated in virtue of multi-material 3D printing. The printed graded plates had accurate size, smooth surface, and good interface. The strains of two graded plates under uniaxial tension were measured experimentally using strain gages. The stresses were calculated within the range of linear elastic from the measured strains and compared with analytical theory. It is found that the experimental results are consistent with the theoretical results, and both of them indicate that the stress concentration around the hole reduces obviously in graded plates with radially increasing Young’s modulus, in comparison with that of perforated homogenous plates. The successful experiment in the paper provides a good basis and support for the establishment of theoretical models and promotes the in-depth development of the research field of stress concentration in functionally graded plates.

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