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![Various Rounded corner equilateral triangular shapes for different í µí¼ ¶ Shape functions for parabolically curved orthotropic triangular section (Fig.45) í µí± 1 = í µí¼(2í µí¼ − 1); í µí± 2 = í µí¼(2í µí¼ − 1); í µí± 3 = (1 − í µí¼ − í µí¼)(1 − 2í µí¼ − 2 í µí¼) (144) í µí± 4 = 4í µí¼í µí¼; í µí± 5 = 4í µí¼(1 − í µí¼ − í µí¼); í µí± 6 = 4í µí¼(1 − í µí¼ − í µí¼) For any ′í µí»¼′ the coordinates of the equilateral triangular plate with curved corners and the radius of the inner circle a=1 is shown in Fig.44 and the coordinates of the six nodes are given for í µí»¼ = 0.4 as í µí±¥ í µí± = [1 , −0.5, −0.5, 1 1+√í µí»¼ , − 2 1+√í µí»¼ , 1 1+√í µí»¼ ] = [1 − 0.5 − 0.5 0.6125 − 1.225 0.6125] (145a) í µí±¦ í µí± = [0 , 0.866 , −0.866, √3 1+√í µí»¼ , 0 , −√3 1+√í µí»¼ ] = [0 0.866 − 0.866 1.061 0 − 1.061]](publication/378102870/figure/fig3/AS:11431281223000287@1707498189684/arious-Rounded-corner-equilateral-triangular-shapes-for-different-i-i14-Shape-functions.png)
Various Rounded corner equilateral triangular shapes for different í µí¼ ¶ Shape functions for parabolically curved orthotropic triangular section (Fig.45) í µí± 1 = í µí¼(2í µí¼ − 1); í µí± 2 = í µí¼(2í µí¼ − 1); í µí± 3 = (1 − í µí¼ − í µí¼)(1 − 2í µí¼ − 2 í µí¼) (144) í µí± 4 = 4í µí¼í µí¼; í µí± 5 = 4í µí¼(1 − í µí¼ − í µí¼); í µí± 6 = 4í µí¼(1 − í µí¼ − í µí¼) For any ′í µí»¼′ the coordinates of the equilateral triangular plate with curved corners and the radius of the inner circle a=1 is shown in Fig.44 and the coordinates of the six nodes are given for í µí»¼ = 0.4 as í µí±¥ í µí± = [1 , −0.5, −0.5, 1 1+√í µí»¼ , − 2 1+√í µí»¼ , 1 1+√í µí»¼ ] = [1 − 0.5 − 0.5 0.6125 − 1.225 0.6125] (145a) í µí±¦ í µí± = [0 , 0.866 , −0.866, √3 1+√í µí»¼ , 0 , −√3 1+√í µí»¼ ] = [0 0.866 − 0.866 1.061 0 − 1.061]
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This study focuses on the determination of torsional rigidity and maximum shear stresses in arbitrarily shaped isotropic and orthotropic composite sections with functional grading of material. A series of numerical examples are solved to validate this approach, with a comprehensive parametric study also conducted. The paper presents the practical a...
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