Three-dimensional vibrations of cracked rectangular parallelepipeds of functionally graded material

An Extended Cell-Based Smoothed Three-Node Mindlin Plate Element (XCS-MIN3) for Free Vibration Analysis of Cracked FGM Plates

“…In addition, to further illustrate the robustness of the proposed method, the results are compared with those by X-MIN3 which is a combination of X-FEM and conventional three-node Mindlin plate element. It can be seen from the table that for many cases of conditions, numerical results solved by the XCS-MIN3 agree well with those by Huang et al [2013]. It is worthy to note that Huang used a hybrid of mathematically complete orthogonal polynomials and 3D-solid elements which are high-ordered elements.…”

“…It can be seen that in spite of using only two-dimensional (2D)-triangular element, the obtained results by XCS-MIN3 are approximately equal to those by Huang et al [2013] which uses 3D element for both thick and thin plates. This proves the efficiency of using such a shear locking free method for free vibration analysis of thin/thick cracked FGM plates.…”

“…Two cases of thin plate with thickness ratio h/a = 0.02 and thick plate with h/b = 0.1; crack inclination angles α varies from 0 • to 45 • ; crack length ratio d/b varies from 0 to 0.5; gradient index n = 5; crack location c y /b = 0.5 are solved. The results are shown in Table 5 compared to those by Huang et al [2013] to verify the correctness of the novel method.…”

“…(3). The first five nondimensionalized frequencies of CFCF rectangular Al/ZrO 2 with finite element mesh of 34 × 34 are summarized in Table 2 in comparison to those obtained by Huang et al [2013]. In addition, to further illustrate the robustness of the proposed method, the results are compared with those by X-MIN3 which is a combination of X-FEM and conventional three-node Mindlin plate element.…”

“…[Huang et al 2011a[Huang et al , 2011b[Huang et al , 2011c used the Reddy TSDT to propose the accurate first-of-its-kind solutions for the vibration of side-cracked FGM thick plate using Ritz technique. Huang et al [2013] cracks. It can be seen from the literature that studies related to vibration analysis of cracked FGM plates using shear-locking-free triangular plate elements is somewhat omitted.…”