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Volume 30, Number 1, January10 2019

In this research, an efficient mixed mode I/II fracture criterion is developed for fracture investigation of orthotropic materials wherein crack is placed along the fibers. This criterion is developed based on extension of well-known Maximum Tensile Stress (MTS) criterion in conjunction with a novel material model titled as Equivalent Reinforced Isotropic Model (ERIM). In this model, orthotropic material is replaced with an isotropic matrix reinforced with fibers. A comparison between available experimental observations and theoretical estimation implies on capability of developed criterion for predicting both crack propagation direction and fracture instance, wherein the achieved fracture limit curves are also compatible with fracture mechanism of orthotic materials. It is also shown that unlike isotropic materials, fracture toughness of orthotic materials in mode I cannot be introduced as the maximum load bearing capacity and thus new fracture mechanics property, named here as maximum orthotropic fracture toughness in mode I is defined. Optimum angle between crack and fiber direction for maximum load bearing in orthotropic materials is also defined.

Key Words
orthotropic materials; fracture criterion; mixed mode; reinforced isotropic material; maximum tangential stress criterion

Faculty of New Sciences & Technologies, University of Tehran, Tehran, Iran.

This work presents the buckling investigation of functionally graded plates resting on two parameter elastic foundations by using a new hyperbolic plate theory. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modelled with only four unknowns and which is even less than the first order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT) by introducing undetermined integral terms, hence it is unnecessary to use shear correction factors. The governing equations are derived using Hamilton's principle and solved using Navier's steps. The validation of the proposed theoretical model is performed to demonstrate the efficacy of the model. The effects of various parameters like the Winkler and Pasternak modulus coefficients, inhomogeneity parameter, aspect ratio and thickness ratio on the behaviour of the functionally graded plates are studied. It can be concluded that the present theory is not only accurate but also simple in predicting the critical buckling loads of functionally graded plates on elastic foundation.

Key Words
functionally graded material; Winkler-Pasternak elastic foundation; new plate theory; buckling analysis; analytical modeling

(1) Kheira Soltani, Mohamed Benguediab:
Department of Mechanical Engineering, Faculty of Technology, University of Sidi Bel Abbes, Algeria;
(2) Aicha Bessaim, Mohammed Sid Ahmed Houari:
University Mustapha Stambouli of Mascara, Faculty of Sciences and Technology, Civil Engineering Department, Mascara, Algeria;
(3) Mohammed Sid Ahmed Houari:
Centre of Excellence for Advanced Materials Research, King Abdulaziz University, Jeddah, 21589, Saudi Arabia;
(4) Kheira Soltani, Mohamed Benguediab:
Faculty of Technology, Laboratory of Materials and Reactive Systems (LMRS), University of Sidi Bel-Abbes, Algeria;
(5) Abdelhakim Kaci:
Universite Dr Taher Moulay Saida - Algeria, Département de Génie Civil et Hydraulique, Algeria;
(6) Aicha Bessaim, Mohammed Sid Ahmed Houari, Abdelhakim Kaci, Abdelouahed Tounsi:
Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria;
(7) Abdelouahed Tounsi:
Laboratoire de Modélisation et Simulation Multi-échelle, Faculté des Sciences, Département de Physique, Université de Sidi Bel Abbes, Algeria;
(8) Mohammed Sh Alhodaly:
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.

In the present study, the various dynamic properties of MWCNT embedded fiber reinforced polymer uniform and tapered composite (MWCNT-FRP) plates are investigated. Various configurations of a tapered composite plate with ply-drop off and uniform composite plate have been considered for the development of the finite element formulation and experimental investigations. First order shear deformation theory (FSDT) has been used to derive the kinetic and potential energy equations of the hybrid composite plates by including the effect of rotary inertia, shear deformation and non-uniformity in thickness of the plate. The governing equations of motion of FRP composite plates without and with MWCNT reinforcement are derived by considering a nine- node rectangular element with five degrees of freedom (DOF) at each node. The effectiveness of the developed finite element formulation has been demonstrated by comparing the natural frequencies and damping ratio of FRP composite plates without and with MWCNT reinforcement obtained experimentally. Various parametric studies are also performed to study the effect of CNT volume fraction and CNT aspect ratio of the composite plate on the natural frequencies of different configurations of CNT reinforced hybrid composite plates. Further the forced vibration analysis is performed to compare the dynamic response of the various configurations of MWCNT-GFRP composite plate with GFRP composite plate under harmonic excitations. It was observed that the fundamental natural frequency and damping ratio of the GFRP composite plate increase approximately 8% and 37% respectively with 0.5wt% reinforcement of MWCNT under CFCF boundary condition. The natural frequencies of MWCNT-GFRP hybrid composite plates tend to decrease with the increase of MWCNT volume fraction beyond 2% due to agglomeration of CNT's. It is also observed that the aspect ratio of the CNT has negligible effect on the improvement of dynamics properties due to randomly orientation of CNT's.

Key Words
CNT reinforced composite plates; Modal analysis; vibration; dynamic characterization

(1) Jakkamputi Lakshmipathi:
School of Mechanical and Building sciences Engineering, Vellore Institute of Technology (VIT), Chennai 600127, Tamil Nadu, India;
(2) Rajamohan Vasudevan:
School of Mechanical Engineering, Vellore Institute of Technology (VIT), Vellore 632014, Tamil Nadu, India.

The aim of this paper is to present new and an efficient optimization algorithm called Jaya for the optimum mass of braced dome structures with natural frequency constraints. Design variables of the bar cross-section area and coordinates of the structure nodes were used for size and shape optimization, respectively. The effectiveness of Jaya algorithm is demonstrated through three benchmark braced domes (52-bar, 120-bar, and 600-bar). The algorithm applied is an effective tool for finding the optimum design of structures with frequency constraints. The Jaya algorithm has been programmed in MATLAB to optimize braced dome.

Key Words
Jaya algorithm; size and shape optimization; frequency constraints; braced dome structure

(1) Maksym Grzywiński:
Czestochowa University of Technology, Faculty of Civil Engineering, 42200 Czestochowa, Poland;
(2) Tayfun Dede, Yaprak Itır Özdemir:
Karadeniz Technical University, Department of Civil Engineering, Trabzon, Turkey.

This paper deals with the static analysis of axially functionally graded rectangular plates. It is assumed that the flexural rigidity of the plate varies exponentially along one of the plate's in-plane dimensions. Both an analytical approach and a numerical method are utilized to solve the problem. The analytical solution is obtained by using the Green's function method. To employ this approach, the adjoint boundary value problem is established. Then, exact solutions for deflection of the plate for different boundary conditions are found. In another way, a finite element formulation for the problem is developed. In order to demonstrate the validity of the Authors' formulation, the results obtained via both mentioned schemes are compared with each other for functionally graded plates and with results of previously published works for homogeneous plates. The effect of plate parameters on the response of the plate is also investigated. To remind the research background, a brief review on the application of Green's function method in plates' analysis and functionally graded plates is also presented.

Key Words
Green\'s function method; deflection; axially functionally graded rectangular plate; exact solution; finite element formulation

(1) Mohammad Rezaiee-Pajand, Ahmad Aftabi Sani:
Department of Civil Engineering, Ferdowsi University of Mashhad, Iran;
(2) Seyed Mojtaba Hozhabrossadati:
Department of Civil Engineering, Toos Institute of Higher Education, Mashhad, Iran.

Numerous problems have always vexed engineers with buckling, corrosion, bending, and over-loading in damaged steel structures. The present study aims to study the possible effects of Carbon Fiber Reinforced Polymer (CFRP) for strengthening deficient Steel Square Hollow Section (SHS) columns. To this end, the effects of axial loading, stiffness values, axial displacement, the shape of deficient on the length of steel SHS columns were evaluated based on a detailed parametric study. Ten specimens were tested to failure under axial compression in laboratory and simulated by using Finite Element (FE) analysis based on numerical approach. The results indicated that the application of CFRP sheets resulted in reducing stress in the damage location and preventing or retarding local deformation around the deficiency location appropriately. In addition, the retrofitting method could increase loading the carrying capacity of specimens.

Key Words
Square Hollow Section (SHS); deficiency; CFRP; steel column; strengthening

(1) Mehdi Shahraki, Mohammad Reza Sohrabi, Gholamreza Azizyan:
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran;
(2) Kambiz Narmashiri:
Department of Civil Engineering, Zahedan Branch, Islamic Azad University, Zahedan, Iran.

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