On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis. New results of critical thermal buckling temperature rise of FGPs with internal defects are presented. An efficient and accurate thermal strain XIGA/level set using FSDT has been developed for FGPs with internal defects.
This paper thus focuses particularly on the study of the thermal buckling phenomenon of FGPs with internal defects under temperature variation. It is fairly well covered in the literature investigating the thermal buckling behavior of FGPs. The effect of geometric imperfections on the thermal buckling of FGP was investigated by Shariat and Eslami [10].
12] investigated the mechanical and thermal buckling behavior of FGPs using first-order shear deformation plate theory (FSDT) in combination with the element-free kp-Ritz method. Nevertheless, studies on thermal buckling failure behavior of FGPs with internal defects are quite rare. In this paper, we investigate the thermal buckling behavior of FGPs with internal defects such as cracks or cuts using NURBS-based XIGA with level sets and the FSDT.
In Section 3, XIGA formulation for thermal buckling analysis of plates with internal defects is derived.
Numerical results and discussions
4, and additionally presented in Table 3, shows us a strong influence of the boundary conditions on the CBTR. The CBTR of the CCCC is much larger than that of an SSSS as well as other boundary conditions. 4 Effect of crack and boundary conditions on the CBTR as a function of the volume fraction exponent of a rectangular Al/Al2O3 plate (h/b = 0.1).
Next, the study on the variation of the CBTR affected by the crack size is now investigated. Fig.5 shows the present numerical results of the CBTR as a function of crack sizes of an Al/Al2O3 plate with an edge crack with n=1 for various boundary conditions. 5 Effect of crack size on the CBTR of a rectangular Al/Al2O3 plate with an edge.
The present numerical results of the CBTR show that increasing the volume fraction exponent n causes a small decrease in the critical buckling load. Effect of the oblique angle of crack on the CBTR of a fully simple supported Al/ZrO2. On the contrary, the present numerical results accounted for SFSF plate show no effect of the crack size on the CBTR.
7 Effect of crack size and boundary condition on the CBTR of a square Al/ZrO2 plate for different boundary conditions. We focus our attention on the numerical investigation of the effects of different gradient indices, skew angles and the boundary conditions on the CBTR. The effects of the gradient index and the boundary conditions on the CBTR are investigated.
Effect of volume fraction exponent and boundary conditions on the CBTR of an inclined Al/Al2O3 plate with an edge crack (θ=60o). Convergence study of CBTR for a simply supported square Al/ZrO2 plate with circular cut at the center to calculate different volume fraction exponents. As expected, CCCC tiles give a higher value of CBTR compared to a SSSS.
12 Effect of the radius to length aspect ratio (2r/a) and the volume fraction exponent on the CBTR of a SSSS square Al/ZrO2 FGP. 13 Effect of the boundary conditions on the CBTR of a SSSS square Al/ZrO2 FGP (2r/a =0.4) modified by the volume fraction exponent. The numerical results of CBTR for a simply supported FGM slab are reported in Table 7.
Also in Table 7, interestingly, the volume fraction exponent of the CBTR changes significantly with different locations of the recess.
Conclusions
In this formulation, the trimmed NURBS surface to describe the geometric structure with cut-outs is no longer necessary, since the internal discontinuity is mesh-independent, resulting from the use of level arrays. The accuracy of the CBTR obtained by the developed XIGA is high and in good agreement with the reference solutions for thin and medium-thick plates with internal defects. The effects of boundary conditions and volume fraction exponents on CBTR FGP are significant.
It was found that the CBTR behavior of square plates with an inclined central crack is symmetrical with respect to crack orientation α=45o and decreases with increasing crack orientation α. Increasing the cutout size and the gradient index n leads to a decrease in the CBTR of the FGP. A notch or defect closer to the plate boundary causes a larger CBTR than a notch in the center.
Knowledge derived from the study can be useful for the design and development of the FGMs and FGP structures in advanced engineering. TT Yu gratefully acknowledges the supports from the National Natural Science Foundation of China (Grant No.) and the National Sci-Tech Support Plan of China (Grant No. 2015BAB07B10). Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory.
Refined and simple shear strain theory for thermal buckling of solar functionally graded panels on an elastic foundation. Three-dimensional thermal deflection analysis of functionally graded arbitrary planar quadrilateral plates using the differential quadrature method. Thermal buckling of functionally graded inclined and trapezoidal plates with different boundary conditions using the element-free Galerkin method.
A parametric study of buckling of functionally graded material plates with internal discontinuities using the partition of unit method. NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter. Isogeometric lock-free plate element: A simple first-order shear deformation theory for functionally graded plates.
