• Advances in nano research
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• v.3 no.4
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• pp.177-191
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• 2015

In this article, various higher-order shear deformation theories (HSDTs) are developed for bending and buckling behaviors of nanowires including surface stress effects. The most important assumption used in different proposed beam theories is that the deflection consists of bending and shear components and thus the theories have the potential to be utilized for modeling of the surface stress influences on nanowires problems. Numerical results are illustrated to prove the difference between the response of the nanowires predicted by the classical and non-classical solutions which depends on the magnitudes of the surface elastic constants.

• Structural Engineering and Mechanics
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• v.8 no.3
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• pp.233-242
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• 1999

In the present study, the elasto-plastic analysis of prismatic plate structures subjected to pure bending is carried out using the finite strip method. The end cross-sections of the structure are assumed to remain plane during deformation, and the compatibility along corner lines is ensured by choosing proper displacement functions. The effects of both the initial geometrical imperfections and residual stresses due to fabrication are included in the combined geometrically and materially nonlinear simulation. The von-Mises yield criterion and the Prandtl-Reuss flow theory of plasticity are applied in modelling the elasto-plastic behavior of material. Newton-Raphson iterations are carried out as the rotation of the end cross sections of the structure is increased step by step. The parameter representing the overall axial strain of structure is adjusted constantly during the iteration process in order to eliminate the resulting overall axial force on any cross-section of the structure in correspondence with the assumption of zero axial force in pure bending. Several numerical examples are presented to validate the present method and to investigate the effects of some material and geometrical parameters.

• Transactions of Materials Processing
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• v.30 no.6
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• pp.275-283
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• 2021

A parametric study was conducted on the effects of five fundamental design parameters on springback, including die clearance, step height, step width, punch radius, and taper relief in an L-bending process, controlled by the compression force. The experiment was also conducted to verify the usefulness of the parametric study procedure for process design, as well as the finite element predictions. The elastoplastic finite element method was utilized. The L-bending process of the york product, which is a key part of the breaker mechanism, was employed. The deformation of the material was assumed to be due to plane strain. Five samples of each design parameter were selected based on experiences in terms of process design. The finite element predictions were analyzed in detail to show a shortcut towards the process design improvement which can replace the traditional process design procedure relying on trial-and-errors. The improved process design was verified to meet all the requirements and the predictions and experiments were in good agreement.

• Steel and Composite Structures
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• v.31 no.5
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• pp.469-488
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• 2019

We in this paper study nonlinear bending of a functionally graded porous nanobeam subjected to multiple physical load based on the nonlocal strain gradient theory. For more reasonable analysis of nanobeams made of porous functionally graded magneto-thermo-electro-elastic materials (PFGMTEEMs), both constituent materials and the porosity appear gradient distribution in the present expression of effective material properties, which is much more suitable to the actual compared with the conventional expression of effective material properties. Besides the displacement function regarding physical neutral surface is introduced to analyze mechanical behaviors of beams made of FGMs. Then we derive nonlinear governing equations of PFGMTEEMs beams using the principle of Hamilton. To obtain analytical solutions, a two-step perturbation method is developed in nonuniform electric field and magnetic field, and then we use it to solve nonlinear equations. Finally, the analytical solutions are utilized to perform a parametric analysis, where the effect of various physical parameters on static bending deformation of nanobeams are studied in detail, such as the nonlocal parameter, strain gradient parameter, the ratio of nonlocal parameter to strain gradient parameter, porosity volume fraction, material volume fraction index, temperature, initial magnetic potentials and external electric potentials.

• Structural Engineering and Mechanics
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• v.78 no.4
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• pp.439-453
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• 2021

In this work, quasi three-dimensional (quasi-3D) shear deformation theory is presented for bending and dynamic analysis of functionally graded (FG) plates. The effect of varying material properties and volume fraction of the constituent on dynamic and bending behavior of the FG plate is discussed. The benefit of this model over other contributions is that a number of variables is diminished. The developed model considers nonlinear displacements through the thickness and ensures the free boundary conditions at top and bottom faces of the plate without using any shear correction factors. The basic equations that account for the effects of transverse and normal shear stresses are derived from Hamilton's principle. The analytical solutions are determined via the Navier procedure. The accuracy of the proposed formulation is proved by comparisons with the different 2D, 3D and quasi-3D solutions found in the literature.

• Earthquakes and Structures
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• v.20 no.4
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• pp.405-415
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• 2021

Following the dynamic property analysis and elaboration, linear response spectrum analysis (RSA) and response history analysis (RHA) were conducted on a representative hyperbolic cooling towers (HCT) in present study. The seismic responses in tower shell were illustrated in detail, including the internal force amplitude, modal contribution, influence from damping ratio, comparison of results got from RSA and RHA and especially the latitude distributions of internal forces. The results show that the eigenmodes could be classified in a new method into four types according to their mode shapes and only the lateral bending modes and vertical stretching modes are meaningful for horizontal and vertical earthquake correspondingly. The bending modes and seismic deformation display the same feature which is global lateral bending accompanied by minute circular flow displacement of section. This feature also decides the latitude distributions of internal forces as sine or cosine. Moreover, the following method is also proposed for approximate estimation of internal force amplitudes without time-consuming response history analysis: getting the response spectrums of the selected ground accelerations and then comparing values of response spectrums at the natural period of first lateral bending mode because it is always prime dominant for horizontal seismic responses.

• Computers and Concrete
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• v.31 no.3
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• pp.197-206
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• 2023

In this paper, the bending performance of a MSFRHPC (containing steel fiber, polyvinyl alcohol (PVA) fiber, and CW)-reinforced beam was studied for the first time. Introducing a multiscale fiber system increased the first crack load (up to 150%), yield load (up to 50%), and peak load (up to 15%) of reinforced beams. The multiscale fiber system delays cracking of the reinforced beam, reduces crack width of the reinforced beam in normal use, and improves the durability of the beam. Considering yield load and peak load, the reinforcing effect of multiscale fiber on the high-reinforcement ratio beam (1.00%) is better than that on the low-reinforcement ratio beam (0.57%). Introducing fibers slowed the development of cracks in the reinforced beam under bending. With the added hybrid fiber, the deformation concentration of reinforced beams after yield was more significant with concentration in 1 or 2 cracks. A model for predicting the flexural capacity of MSFRHPC-reinforced beams was proposed, considering the action of multiscale hybrid fibers. This research is helpful for structure application of MSFRHPC-containing CW.

• Advances in nano research
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• v.13 no.4
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• pp.393-406
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• 2022

In the present article, functionally graded small-scaled plates based on modified strain gradient theory (MSGT) are studied for analyzing the nonlinear bending and post-buckling responses. Von-Karman's assumptions are applied to incorporate geometric nonlinearity and the first-order shear deformation theory is used to model the plates. Modified strain gradient theory includes three length scale parameters and is reduced to the modified couple stress theory (MCST) and the classical theory (CT) if two or all three length scale parameters become zero, respectively. The Ritz method with Legendre polynomials are used to approximate the unknown displacement fields. The solution is found by the minimization of the total potential energy and the well-known Newton-Raphson technique is used to solve the nonlinear system of equations. In addition, numerical results for the functionally graded small-scaled plates are obtained and the effects of different boundary conditions, material gradient index, thickness to length scale parameter and length to thickness ratio of the plates on nonlinear bending and post-buckling responses are investigated and discussed.

• Structural Engineering and Mechanics
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• v.84 no.2
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• pp.225-238
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• 2022

In order to improve the cracking resistance of reinforced concrete and give full play to the advantages of prefabricated assembly structure in construction, prestressed reinforced concrete composite beam (PRCC) is proposed. Through the bending static test of seven I-shaped beam specimens, the bending failure modes and bearing capacity of PRCC and reinforced concrete composite beam are compared and analyzed, and the effects of prestress size, prestressed reinforcement layout and prestress application sequence on the flexural behavior of PRCC beams are studied. The results show that the cracking load and ultimate load of PRCC beams significantly increased after prestressing, and prestressed tendons can effectively control the crack development. With the increase of prestressing degree, the deformation resistance and bending stiffness of PRCC beams are increased. The application sequence of prestress has little influence on the mechanical properties of PRCC beams. The crack width, stiffness and normal section bearing capacity of PRCC beam are analyzed, and the calculated results are in good agreement with the experimental results.

• Computers and Concrete
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• v.33 no.1
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• pp.91-102
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• 2024

Beam-shaped components commonly rotate along a fixed axis when massive mechanical structures like rotors, jet engine blades, motor turbines, and rotating railway crossings perform their functions. For these structures to be useful in real life, their mechanical behavior is essential. Therefore, this is the first article to use the modified shear deformation theory type hyperbolic sine functions theory and the FEM to study the static bending response of rotating functionally graded GPL-reinforced composite (FG-GPLRC) beams with initial geometrical deficiencies in thermal media. Graphene platelets (GPLs) in three different configurations are woven into the beam's composition to increase its strength. By comparing the numerical results with those of previously published studies, we can assess the robustness of the theory and mechanical model employed in this study. Parameter studies are performed to determine the effect of various geometric and physical variables, such as rotation speed and temperature, on the bending reactions of structures.