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A review of theories for the modeling and analysis of functionally graded plates and shells

Stress, vibration and buckling analyses of FGM plates—A state-of-the-art review

The objective of this paper is to provide the theoretical background and illustrative examples for elastic buckling analysis of cold-formed steel members with general boundary conditions as implemented in the forthcoming update to CUFSM. CUFSM is an open source finite strip elastic stability analysis program freely distributed by the senior author. Although the finite strip method presents a general methodology, the conventional implementation (e.g. CUFSM v 3.13 or earlier) employs only simply-supported boundary conditions. In this paper, utilizing specially selected longitudinal shape functions, the conventional finite strip method is extended to general boundary conditions, including the conventional case: simply-simply supported, as well as: clamped-clamped, clamped-simply supported, clamped-free, and clamped-guided. The solution remains semi-analytical as the elastic and geometric stiffness matrices are derived in a general form with only specific integrals depending on the boundary conditions. An example of the stability solution is provided. The selection of longitudinal terms to be included in the analysis is discussed in terms of balancing accuracy with computational efficiency. Also herein, the constrained finite strip method is extended to general boundary conditions. Both modal decomposition and identification can be carried out based on the new bases developed for the constrained finite strip method, and illustrative examples are provided. This extension of CUFSM is intended to aid the implementation of the direct strength method to the case of general boundary conditions.

/pdf/buckling-analysis-of-cold-formed-steel-members-with-general-mpqu0wj21j.pdf

Buckling Analysis of Cold-formed Steel Members with General Boundary Conditions Using CUFSM Conventional and Constrained Finite Strip Methods

https://northumbria-test.eprints-hosting.org/id/document/265204

A review of continuum mechanics models for size-dependent analysis of beams and plates

Buckling of plates with different end conditions using the finite strip method

In the present article the mechanical instability and free vibration of FGM micro-plate based on the modified strain gradient theory were studied using the spline finite strip method. By daily increase in the application of micro-scale structures, developing theories were become essential to account in a way for the size-reduction effect. The modified strain gradient theory based on three length scale parameters, has the capability of evaluating structures at the micro size level. Considering the obtained results, it was clear that increasing the length-scale parameter would increase the critical buckling load and the vibration frequency, similar to the macroscopic case. In addition, increasing the power of volume fraction module decreases the critical load and the natural frequency of micro plate. Finally, the effect of length-scale parameter, boundary conditions, volume fraction module and dimensions of the micro-plate on critical loading and natural frequency of micro-plate were studied.

Buckling and free vibration of the FGM thin micro-plate based on the modified strain gradient theory and the spline finite strip method

Exact free vibration analysis of axially moving viscoelastic plates

In this research, concrete beams were strengthened with carbon-fiber-reinforced polymer (CFRP) laminate strips that were placed in precut grooves on the concrete surface. Five simple-span reinforced concrete (RC) beams were tested. Among these specimens, one served as a reference beam and was not strengthened, one was tested after being strengthened with nonprestressed near-surface-mounted (NSM) CFRP laminates, and the remaining three were strengthened with NSM CFRP laminates that had been prestressed to 5, 20, and 30% of the nominal ultimate strain of the strips. The test results indicate that the prestressed beams more effectively improved the cracking and yielding loads than the nonprestressed strengthened specimen. In addition to a higher cracking load, the prestressed strengthened specimens had cracks with a more limited distribution and width. Furthermore, the prestressed strengthened beams had up to a 15% higher ultimate load-carrying capacity than the nonprestressed specimen, and their failures corresponded to lower deflections.

Mojtaba Azhari

Papers

Buckling of plates with different end conditions using the finite strip method

Buckling and free vibration of the FGM thin micro-plate based on the modified strain gradient theory and the spline finite strip method

Exact free vibration analysis of axially moving viscoelastic plates

Investigation of RC Beams Strengthened with Prestressed NSM CFRP Laminates

Free vibration of moving laminated composite plates