A new higher-order mixed four-node quadrilateral finite element for static bending analysis of functionally graded plates

Bending, buckling and free vibration analyses of shallow-to-deep FG curved sandwich beams using a global–local refined shear deformation theory

“…The arrays of 𝒖 ̂11 𝑒 , 𝒖 ̂33 𝑒 , 𝒖 ̂22 𝑒 , 𝜳 𝑢 11 , 𝜳 𝑢 33 , and 𝜳 𝑢 22 are not stated here for the sake of briefness. For more information about these submatrices, readers are referred to Ref.…”

“…ˆê e   uu (22) where NC is the number of layers; e denotes the number of elements, and se is the element length along the scurve.…”

“…Due to neglecting the shear effect, Euler-Bernoulli, and Timoshenko beam theory are not accurate enough to predict the structural responses of FG beams, especially for thick ones [22][23][24][25]. These limitations inclined the researchers to develop different refined and higher-order beam theories (HBTs).…”

Guided Wave-Based Damage Detection of Square Steel Tubes Utilizing Structure Symmetry

“…Ultrasonic guided wave (UGW) is a kind of ultrasonic wave that can propagate in structural members with finite boundaries, such as thin plates [2][3][4][5][6][7][8][9], tubes [10][11][12][13][14][15][16], bars [17], other member types [18][19][20]. When encountering small defects or damages in structures, wave scattering and reflection will occur.…”

“…With regard to the damage detection of square steel tubes using UGWs, Wan [1] investigated frequency dispersion characteristics and selected the appropriate guided wave mode to inspect through-hole and slot damages. Ultrasonic guided wave (UGW) is a kind of ultrasonic wave that can propagate in structural members with finite boundaries, such as thin plates [2][3][4][5][6][7][8][9], tubes [10][11][12][13][14][15][16], bars [17], other member types [18][19][20]. When encountering small defects or damages in structures, wave scattering and reflection will occur.…”