Buckling of Simply Supported Skew Plates

Elastic Shear Buckling Coefficients for Oblique Plates

“…Figure 6 compares the shear buckling coe cients obtained by the method presented in this study with those obtained by Wittrick [14], Kennedy and Prabhakara [18], and Durvasula [21]. Kennedy and Prabhakara [18] obtained the shear buckling coefficients in the positive and negative directions for simply supported parallelograms with angles of 15 °, 30 °, 45 °, and 60 °with aspect ratios of 0.5, 1.0, 1.5, and 2.0, respectively.…”

“…Kennedy and Prabhakara [18] obtained the shear buckling coefficients in the positive and negative directions for simply supported parallelograms with angles of 15 °, 30 °, 45 °, and 60 °with aspect ratios of 0.5, 1.0, 1.5, and 2.0, respectively. Durvasula [21] also obtained shear buckling coefficients in the positive and negative directions for simply supported parallelograms with angles of 15 °, 30 °, 45 °, and 60 °with aspect ratios of 0.5, 1.0, 1.5, and 2.0, respectively. Wittrick [14] obtained a shear buckling coefficient in the negative direction for clamped supported parallelograms with an angle of 45 °and an aspect ratio of approximately 0.8 to 2.4. e analytical results presented by Wittrick [14] and Kennedy and Prabhakara [18] were almost the same as those presented in this study, although the displacement function and coordinate system settings were different from those in this study.…”

“…However, Wittrick [14] did not present larger critical shear buckling coefficients and Kennedy and Prabhakara [18] underestimated the elastic shear buckling coefficient in the negative direction. It was observed that the analysis results presented by Durvasula [21] overestimated the elastic shear buckling strength; such discrepancies were attributed to the failure in satisfying all the boundary conditions and an insufficient matrix size.…”

“…Figure 3 illustrates the buckling displacement determined using the proposed function (equations ( 1) and ( 2)) for m n 1. Previous studies [13][14][15][16][17][18][19][20][21][22][23][24][25] on the buckling of oblique plates de ned a coordinate system along the oblique edges, whereas the present study employed a Cartesian coordinate system to handle the stresses easily. On all edges of the oblique plate, both displacement functions are zero displacement (w 0); the displacement function for simply supported edges allows rotation on the edges (zw/zx ≠ 0, zw/zx ≠ 0) and the displacement function for clamped supported edges restrains the rotation on the edges (zw/zx 0, zw/zx 0).…”

“…Ashton [19] obtained the elastic buckling strength of oblique plates with clamped supported edges subjected to combined stresses using the Ritz method. In addition to these studies, other methods for calculating the elastic buckling strength based on energy methods, such as the Galerkin and Raleigh-Ritz methods, have also been presented [20][21][22][23][24][25]. However, these calculation methods were not convenient: they provided tables or graphical charts of the elastic buckling coe cients at speci c angles or aspect ratios or required complex matrix equations to be solved.…”