Abstract
Abstract The main goal of this research is to study the postbuckling behavior of nonlocal functionally graded beams. Eringen’s nonlocal differential model is used to evaluate the influence of the material length scale in the bending response. An improved shear deformation beam theory with five independent parameters is utilized, which is suitable for the use of 3D constitutive equations. A finite element model is derived with spectral high-order interpolation functions to avoid shear locking. The formulation is verified by comparing the present results with the ones found in the literature. Functionally graded beams with different boundary conditions, nonlocal parameters, and power law indices are analyzed. It is shown that the present model can accurately predict the behavior of nonlocal beams due to the use of high-order terms in the displacement field in comparison with classical beam formulations. Finally, new benchmark problems are analyzed to show the capabilities of the present model to evaluate the effect of the nonlocal parameter and the power law index on postbuckling beam behavior.
Highlights
Over the last two decades, the interest in generalized continuum mechanical models capable of predicting the response of structural elements with material length scales has increased
We have presented a post-buckling study of functionally graded nonlocal beams
The formulation was based on an improved beam theory (IFSDT) with five independent parameters that account for thickness stretch and 3D constitutive relations
Summary
Over the last two decades, the interest in generalized continuum mechanical models capable of predicting the response of structural elements with material length scales has increased. A review of this can be found in the work of Chandel et al (2020), who provided an overview of the different models of analysis of nanostructures under different loadings and boundary conditions, as well as their application in different fields. According to Srinivasa and Reddy (2017), within non-classical continuum mechanics, Eringen’s theory can be categorized as a strain based nonlocal theory. Other examples of non-classical models with displacements as independent variables are high strain gradient models (see Toupin, 1964; Mindlin and Eshel, 1968; Yang et al, 2002). Other group of nonlocal theories is referred to as “peridynamics,” and it is based on the original work of Silling (2000). For a comprehensive review of this theory, see the work of Silling and Lehoucq (2010)
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