Thin–Walled Structures 157 (2020) 107139 Available online 25 September 2020 0263-8231/© 2020 Elsevier Ltd. All rights reserved. Static bending analysis of functionally graded polymer composite curved beams reinforced with carbon nanotubes Pouyan Talebizadehsardari a, b , Arameh Eyvazian c , Mohammed Asmael d , Behrouz Karami e , Davood Shahsavari e , Roohollah Babaei Mahani f, g, * a Metamaterials for Mechanical, Biomechanical and Multiphysical Applications Research Group, Ton Duc Thang University, Ho Chi Minh City, Viet Nam b Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Viet Nam c Mechanical and Industrial Engineering Department, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar d Department of Mechanical Engineering, Eastern Mediterranean University, Famagusta, North Cyprus Via Mersin 10, Turkey e Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran f Institute of Research and Development, Duy Tan University, Da Nang, 50000, Viet Nam g Faculty of Civil Engineering, Duy Tan University, Da Nang, 550000, Viet Nam A R T I C L E INFO Keywords: Static analysis Curved beam Carbon nanotubes Nonlocal strain gradient theory Composite structures ABSTRACT This article deals with the static bending response of a functionally graded polymer composite (FG-PC) curved beam reinforced with carbon nanotubes (CNTs) subjected to sinusoidal and uniform loads. The effective material properties of beam are approximated according to modifed rule of mixture. Four types of CNT distribution are also considered. Assuming Timoshenko beam theory and a higher-order strain gradient theory, size-dependent equilibrium equations are extracted. Using Navier solution procedure, nonlocal strain gradient governing equations are solved for simply-supported edges. Ultimately, numerical results are expanded to show the in- fuence of weight fraction and distribution patterns of CNTs, small scale parameters, and opening angle on the static bending response of CNTs reinforced nanocomposite curved beam. 1. Introduction In thin-walled structures application, curved beams are of great importance and are often used in helicopters, rockets, and vessels. Moreover, for the reliable design of thin plates and shells, curved beams have been utilized as stiffeners for improving their loading capacity. As another point of view, since there is a relationship between external load and principle curvature plane, this structure could be considered as an arch. Due to the type of external load, the analysis may be static or dynamic. Static analysis is associated with defection, stress and critical buckling load responses. Although a great number of researches use numerical methods, semi-analytical methods and analytical closed-form solutions have been applied in the static analysis of curved beams to tackle with historical problems of civil and mechanical engineering [1–3]. The size-dependent mechanical characteristics of such structures have attracted signifcant attention in recent years with the advent of micro/nano-structures [4,5]. Recently, both derivations of stress and strain-driven variations for nano-size beams have been reported by Barretta and his co-workers [6–8]. The softening-stiffness mechanism of size-dependency in the bending analysis of FG curved nano-size beams using nonlocal elasticity and Timoshenko beam theories was investi- gated by Hosseini and Rahmani [9]. Then, an analytical nonlocal elas- ticity model was developed by Aref and Zenkour to analyze the static bending of curved nanobeams subjected to a transverse mechanical load [10]. Eringen nonlocal model in conjunction with various beam theories was developed for static bending and buckling analyses of simply-supported thick curved nanobeams by Ganapathi and Polit [11]. For another size effect assumption, the stiffness-enhancement mecha- nism of size-dependency was analyzed for bending analysis of FG curved micro-size beams using strain gradient theory by Zhang et al. [12]. Karami et al. [13] showed that micromechanical models or type of ho- mogenization scheme are crucial factors for accurate mechanics of FG curved microbeams [13]. Because of some non-standard boundary conditions, there is a discussion regarding the application of nonlocal strain gradient theory (NSGT) as a combination of strain-driven and stress-driven nonlocal theories. Barretta et al. [6,14] presented * Corresponding author.Institute of Research and Development, Duy Tan University, Da Nang, 50000, Viet Nam. E-mail addresses: ptsardari@tdtu.edu.vn (P. Talebizadehsardari), behrouz.karami@miau.ac.ir (B. Karami), shahsavari.davood@miau.ac.ir (D. Shahsavari), roohollahbabaeimahani@duytan.edu.vn (R.B. Mahani). Contents lists available at ScienceDirect Thin-Walled Structures journal homepage: http://www.elsevier.com/locate/tws https://doi.org/10.1016/j.tws.2020.107139 Received 22 April 2020; Received in revised form 1 September 2020; Accepted 10 September 2020