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CONTENTS
Volume 78, Number 6, June25 2021
 


Abstract
In this work, we propose a novel method associating a weak form Moving Least Square (MLS) method, also called Element Free Galerkin (EFG) method, and a strong form MLS method to solve the structural problems in two-dimensional elasticity. Therefore we use the displacement compatibility and the force equilibrium conditions on the interface to ensure the coupling between meshfree weak form method and meshfree strong form method. The strong form MLS method is easy to implement and computationally efficient, but it can be unstable and less precise for problems with Neumann boundary conditions. On the other hand, the weak form MLS method ensures very good stability and excellent precision, but it requires the numerical integration which makes this method not "truly" meshless and computationally expensive. Among of the advantages of the proposed method are the following: (i) numerical integrations are avoided for all nodes in the domain of the strong form approximation, (ii) the weak form can be used for nodes on the Neumann boundary, (iii) the strong form can be used in the region of large deformation. Comparative studies with analytical solutions and weak form methods are presented to show the effectiveness and performance of the proposed method.

Key Words
meshfree weak-strong form method; Moving Least Square (MLS); coupling weak-strong forms

Address
Redouane El Kadmiri, Youssef Belaasilia: Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM CASABLANCA), 20670 Casablanca, Morocco;
Sultan Moulay Slimane University, National School of Applied Sciences of Khouribga, LIPIM Laboratory, Khouribga, Morocco
Abdelaziz Timesli: Hassan II University of Casablanca, National Higher School of Arts and Crafts (ENSAM CASABLANCA), 20670 Casablanca, Morocco
M. Saddik Kadiri: Sultan Moulay Slimane University, National School of Applied Sciences of Khouribga, LIPIM Laboratory, Khouribga, Morocco

Abstract
A formulation of a quadratic incompatible quadrilateral element, called DSQK, using a combination of free formulation approach, independent transverse shear strains, and discrete shear constraints, is described in this paper. This new element, which includes transverse shear effects and is valid for thin and thick plates, has 4 nodes and 3 DOFs per node (transverse displacement w and rotations x and y at the corner nodes). The couple between lower order and higher order bending energy is assumed to be zero in the DSQK element to fulfill the constant bending patch test. The independent transverse shear strain is expressed only by second derivatives of the rotations obtained from a unified and integrated kinematic relationship, constitutive law, and equilibrium equations. The validation based on individual element tests, patch tests, and convergence tests deliver good results for thin to thick plates of various geometries.

Key Words
incompatible finite element; DSQK; free formulation; independent transverse shear strain; discrete shear

Address
Irwan Katili: Civil Engineering Department, Universitas Indonesia, Depok 16424, Indonesia

Abstract
The paper aims to revisit shakedown analysis involving temperature-dependent yield stress. Formulations and numerical implementations are focused on truss structures subjected to cyclic thermal and constant mechanical loads. In particular, a systematic approach based on the duality relationship of l-norm and l1-norm is established to state the dual formulations for static and kinematic shakedown analysis of truss structures. Illustrative examples are involved statically indeterminate three-bar and five-bar trusses, respectively. Numerical effort is made to acquire shakedown limit temperature by using the linprog function provided by MATLAB. Furthermore, the finite-element analysis using ABAQUS is also performed for rigorous comparisons.

Key Words
shakedown analysis; cyclic thermal loading; temperature-dependent yield stress; truss structures; Holder inequality; l-norm; l1-norm

Address
S.Y. Leu, Y.H. Chen: Department of Aviation Mechanical Engineering, China University of Science and Technology,
No. 200, Jhonghua St., Hengshan Township, Hsinchu County 31241, Taiwan R.O.C.
K.C. Liao: Department of Biomechatronics Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan R.O.C.

Abstract
In this research, the nanocomposite boxes are simulated using polyurethane (PU) as a thermoplastic polymer with various reinforcements including carbon nanoparticles (CNPs), graphene platelets (GPLs), single-walled carbon nanotubes (SWCNTs), and double-walled carbon nanotubes (DWCNTs), which are as biocompatible and biodegradable. To predict the mechanical and physical properties of each nanocomposite boxes, the molecular dynamics (MDs) method with Materials studio software has been applied. Ultimately, all properties including mechanical and physical properties (Young's modulus, shear modulus, bulk modulus and Poisson's ratio of nanocomposite from CNPs to DWCNTs approximately becomes 5.7, 10.25, 28.63, 96 and 1.39 times, respectively. Then, the stiffness matrix are obtained by Materials studio software. Moreover, the obtained results from this research are validated with the results of the literature. Also, the mechanical and physical properties of nanocomposite are recommended before fabrication. The manufacturing of this nanocomposite is used for biomedical cases such as artificial vessels and piping.

Key Words
carbon nanoparticles; graphene platelets; carbon nanotubes; mechanical and physical properties; molecular dynamics method

Address
Ashkan Farazin, Mehdi Mohammadimehr: Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box 87317-53153, Kashan, Iran
Amirabbas Ghorbanpour-Arani: School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

Abstract
Construction materials such as composites are used recently for the reinforcement and rehabilitation of structures subject to risks of partial or total degradation during their service, which are due to either poor design, overload or a charge assignment. The use of fibers is a new technique which gives additional rigidity and resistance to structures. In this research, we develop an approach which makes it possible to analyze the interfacial constraints which are the cause of the delamination phenomenon at the level of the structure, for a continuous steel beam bonded by a FRP laminate plate, under thermo-mechanical loading coupled with the shear lag model. In such plated beams, shear forces develop in the bonded beam and these will be transferred to the FRP plate via the adhesion technique. Thus, the interfacial shear stress and normal stress will develop consequently, and debonding may occur at the FRP plate ends due to high interfacial stress values in this area. This original research aims to study the debonding phenomenon using an analytical model, in order to identify the interfacial stresses of a continuous steel beam strengthened by the FRP plate with taper model, taking into account a new coupled approach of thermomechanical loading effect. Finally, numerical comparisons between the existing solutions and the present solution enable a clear appreciation of the effects of various parameters. This article explores the effects of various parameters related to the subject, such as the effect of thermal loading, geometrical and physical properties, on the stress behavior of FRP composites. This solution is intended for application to beams made of all kinds of materials bonded with a thin composite plate. For steel I-beam section, a geometrical coefficient q is determined to show the effect of the adherend shear deformations. This research is helpful for the understanding on mechanical behaviour of the interface and design of such structures.

Key Words
interfacial stresses; continuous steel beam; strengthening; shear lag effect; thermal effects; composite materials

Address
Rabahi Abderezak, Hassaine Daouadji Tahar, Benferhat Rabia: Civil Engineering Department, University of Tiaret, Algeria;
Laboratory of Geomatics and Sustainable Development, University of Tiaret, Algeria
Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; LMH Laboratory, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; Department of Civil and Environmental Engineering, King Fahd University Saudi Arabia

Abstract
Steel frames equipped with beam-only-connected steel panel wall (SPWF) system is one type of lateral resisting systems. The fundamental period is necessary to calculate the lateral force for seismic design, however, almost no investigations have been reported for the period estimation of SPWF structures, both in theoretically and in codes. This paper proposes a simple theoretical method to predict the fundamental periods of the SPWF structures based on the basic theory of engineering mechanics. The proposed method estimates the SPWF structures as a shear system of steel frames and a shear-flexure system of SPWs separately, and calculates the fundamental periods of the SPWF structures according to the integration of lateral stiffness of the steel frames and the SPWs along the height. Finite element method (FEM) is used to analyze the periods of 45 case steel frames or SPWF buildings with different configurations, and the FEM is validated by the test results of four specimens. The errors cannot be ignored between FEM and theoretical results due to the simplifications. Thus the finial formula is proposed by correcting the theoretical equations. The relative errors between the periods predicted from the final proposed formula and the results of FEM are no more than 4.6%. The proposed formula could be reliably used for fundamental period estimation of new, existing and damaged SPWF buildings.

Key Words
fundamental period; steel panel wall; infilled steel frame; theoretical calculation; finite element

Address
Liqiang Jiang: School of Civil Engineering, Central South University, Changsha 410075, China; National Engineering Laboratory for High-Speed Railway Construction, Central South University, Changsha 410075, China
Xingshuo Zhang: School of Civil Engineering, Central South University, Changsha 410075, China
Lizhong Jiang: School of Civil Engineering, Central South University, Changsha 410075, China; National Engineering Laboratory for High-Speed Railway Construction, Central South University, Changsha 410075, China
Chang He: School of Civil Engineering, Central South University, Changsha 410075, China; National Engineering Laboratory for High-Speed Railway Construction, Central South University, Changsha 410075, China
Jihong Ye: Xuzhou Key Laboratory for Fire Safety of Engineering Structures, China University of Mining and Technology, Xuzhou, 221116, China
Yu Ran: China Academy of Building Research, Beijing, 100013, China

Abstract
This paper describes a series of full range load tests on two-way, edge-clamped reinforced concrete slab panels containing either Class L WWF or Class N deformed bars. Five rectangular slab panels were tested each with two adjacent fully restrained edges and two free edges. A point support was included under the corner of each panel at the intersection of the two free edges. Each slab specimen was loaded by four transverse loads applied symmetrically in the mid-panel region by a deformation-controlled actuator in a stiff testing frame. The continuous edge supports were provided by clamping two adjacent edges in a carefully designed and constructed testing frame. The slabs were instrumented with load cells to measure applied forces and reactions, strain gauges to measure strain in the steel reinforcement and on the concrete surfaces, linear variable displacement transducers and lasers to measure deflections at all stages of loading. The results of the tests are presented and evaluated, with particular emphasis on the strength, ductility and failure mode of the slabs.

Key Words
ductility; reinforced concrete, two-way slabs; low ductility reinforcement; strength; strain localization

Address
Zafer Sakka: Energy and Building Research Center, KISR, Kuwait
R. Ian Gilbert: School of Civil and Environmental Engineering. UNSW, Sydney, Australia

Abstract
In recent years, many researches have been published dealing with the mechanical responses of shells with variable cross-sectional mechanical properties such as sandwich, functionally graded and laminated composites shells. In the present paper, a simple and efficient shear deformation theory is formulated for the free vibration response of functionally graded sandwich shells. The main advantage of this theory is its reduced number of unknowns and their related governing equations and theses tend to be highly compared to others shear deformation shell theories. Two kinds of FG sandwich shells are studied with respect to their geometrical configuration and material properties. The first kind is composed of FG facesheet and homogeneous core and the other is formed by homogeneous facesheet and FG core. The governing equations of motion for the free vibration analysis are obtained using Hamilton's principle. The closed form solutions are sought by using the Navier's method for eigenvalue problems. The accuracy and efficiency of the present theory are established and proved by comparing obtained numerical results with those predicted by other higher order shear deformation shell theories. The influences of various parameters such as material distribution, thickness of the core and the facesheet of sandwich shell and curvature ratios are studied, discussed and reported as significant rate sensitivity to predict the fundamental frequencies of FG sandwich shells.

Key Words
free vibration; sandwich functionally graded material; shear deformation shell theory

Address
Omar Slimani: FIMAS Laboratory, Department of Civil Engineering, Faculty of Technology, Tahri Mohamed University, 08000 Bechar, Algeria
Zakaria Belabed: Department of Technology, Institute of Science and Technology, Ctr Univ Naama, BP 66, 45000 Naama, Algeria; Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Fodil Hammadi: Laboratory of Mechanics, Modeling and Experimentation L2ME, Department of Mechanical Engineering, Tahri Mohamed University, 08000 Bechar, Algeria
Noureddine Taibi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
Abdelouahed Tounsi: Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria; YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea

Abstract
In the current paper, an equational model for generalized thermo-visco-elasticity is set up for such an elastic medium that indicates isotropicity along with two temperatures. The angular velocity for rotating this medium is maintained uniformly. Several generalized thermoelasticity theories have been employed to fulfill the detailing purposes which include; Lord-Shulman (L-S) and Green-Lindsay (G-L) theories with one and two relaxation times respectively, coupled theory, Tzou theory consisting of dual-phase lags (DPL), and lastly Green-Naghdi (G-N II) theory in the absence of energy dissipation. The application of Normal mode examination leads to the attainment of specific articulations for the thought about factors. Some specific cases are additionally talked about with regards to the complexity. Also, Numerical as well as the graphical representation of the factors under consideration has been presented. Examinations are carried out by keeping outcome predictions in mind as anticipated by various theories (L-S, G-N II, G-L, and DPL), rotation, viscosity, and two temperatures.

Key Words
viscosity; generalized thermoelasticity; five theories; rotation; two-temperatures; normal mode analysis

Address
Aamnah M. Alharbi: Department of Mathematics, College of Science, Taif Univeristy, P.O. Box 11099, Taif, 21944, Saudi Arabia
Mohamed I.A. Othman: Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt
Haitham M. Atef: Faculty of Science, Department of Mathematics, Damanhur University, Damanhur, Egypt

Abstract
In this study, we present an efficient coupled method for the doubly curved shell vibration modeling. The proposed model is based on the coupling of the hierarchical p-finite element method and the standard h-finite element method. The helements define the curved boundaries of the shell while the p-elements describe the interior domain. The connectivity between the two discretized domains is assured by the least square method. In comparison to conventional models, the coupled model captures accurately the shell curvilinear boundary with high computational efficiency and small number of elements. The proposed model is validated against both analytical solution and numerical simulation. Doubly curved shell structures with different cutouts are presented to show the robustness, applicability and computational convenience of the proposed coupled approach for complex shell geometries.

Key Words
p-version of FEM; h-version of FEM; coupling; vibration; doubly-curved shell; cutout; curvilinear planform

Address
S.M. Chorfi and A. Houmat: Department of Mechanical Engineering, Faculty of Engineering, University of Tlemcen, B.P. 230, Tlemcen 13000, Algeria


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