In this study, large elastic deflections of beams have been investigated using the theory of nonlocal elasticity. Fundamental equations have been derived for large elastic deflections and small strains in the frame of nonlocal elasticity and the solution has been made by the perturbation method. It has been observed that the difference between large elastic local and non-local deflections and moments grows significantly as the ∕ ratio increases ( is nonlocality parameter, is length of beam). K E Y W O R D Slarge elastic deflections, nanobars, nonlocal elasticity, perturbation method, small scale effect

Due to nonlocal and strain gradient effects with rigid and deformable boundary conditions, the thermal vibration behavior of perforated nanobeams resting on a Winkler elastic foundation (WEF) is examined in this paper. The Stokes transformation and Fourier series have been used to achieve this goal and to determine the thermal vibration behavior under various boundary conditions, including deformable and non-deformable ones. The perforated nanobeams’ boundary conditions are considered deformable, and the nonlocal strain gradient theory accounts for the size dependency. The problem is modeled as an eigenvalue problem. The effect of parameters such as the number of holes, elastic foundation, nonlocal and strain gradient, deformable boundaries and size on the solution is considered. The effects of various parameters, such as the length of the perforated beam, number of holes, filling ratio, thermal effect parameter, small-scale parameters and foundation parameter, on the thermal vibration behavior of the perforated nanobeam, are then illustrated using a set of numerical examples. As a result of the analysis, it was determined that the vibration frequency of the nanobeam was most affected by the changes in the dimensionless WEF parameter in the first mode and the changes in the internal length parameter when all modes were considered.

In this study, equal strength cantilever and simply supported beams made of functionally graded material (FGM) whose material properties vary though the height direction were investigated. These equal strength cantilever FGM beams were loaded with uniformly distributed load and a point load at the tip and simply supported FGM beams were loaded with uniformly distributed loads. They have all variable cross-section and straight axis. For calculating equivalent material properties of FGMs, power law distribution and Mori-Tanaka model were used. A computer program was developed for the analysis of the problem. The dimensionless deflection values for cantilever beams and simply supported beams were obtained for different materials by the help of developed computer program. Obtained results are presented in the form of tables and graphs which may be useful for the researchers.

In this study, deflections of orthotropic beams along the beam length are calculated by using static analysis according to Euler-Bernoulli and Timoshenko beam theories. Since the mechanical properties of the materials change as the orientation angle of fibers changes, the formulation is carried out using the equivalent Young's modulus and the equivalent shear modulus. Orthotropic beams are modeled as isotropic beams by using equivalent moduli. Governing equations are derived. Two numerical examples with different orthotropic materials are given for different boundary and loading conditions. The effect of changing the orientation angle of the fibers on the deflection values is also considered. Orientation angle, material properties, length to depth ratio has been considered as parameters in the static analysis of orthotropic beams. Results are also compared with steel which is an isotropic material and presented in the form of tables and graphs which may be useful.