A new theory for laminated composite plates

Abstract

This work presents a new multilayered laminated composite structure model to predict the mechanical behaviour of multilayered laminated composite structures. This new multilayered structure model describes the shear stress distribution model through the thickness respecting free boundary conditions on the top and bottom surfaces by an exponential function. This model has the same order of complexity as Touratier's model 'Sine', so a shear correction factor is not required like in the first-order shear deformation theory. This model is more precise than all other existing refined theories. This theory is based on the kinematic approach in which the shearing is represented by an exponential function. The virtual power principal is used to deduce the boundary value problem. To verify the precision of the present model, several significant problems on bending, vibration, and buckling of laminated and sandwich structures have been studied. The results by the present model are compared with the exact three-dimensional elasticity theory and with several other well-known theories. The proposed model is found to be more precise for analysing multilayered structures.

Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory

“…The normalized displacement and stresses of the present approach are in excellent agreement with the exact solution [47]. It is seen for thick plate cases (a/h = 4, 10) that the ITSDT yields better results than the HSDT [6,48,49], ESDT [51] and the dTrSDTs [38,39,7] in comparison with the exact solution [47]. For thin plate case (a/h = 100), the difference between the solutions are not significant for all displacement and stresses.…”

“…The obtained results indicate a reasonably good agreement with other available ones for all a/h ratios. The normalized displacement and stresses derived from the present theory are more accuracy than those of HSDT [6] and ESDT [51]. Also, the stresses profiles through the thickness of the three-layer square laminated plate with a/h = 4 and 10, respectively, are again displayed in Fig.…”

“…For a comparison, the normalized displacement and stresses of a four layer simply supported square plate are computed using 17 × 17 B-spline elements. The obtained results of the IGA based on the present theory are compared with those of the several other methods based on other higher-order shear deformation theories such as the closed form solution (CSF) based on the HSDT by Reddy M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT [6], the finite strip method (FSM) based on HSDT by Akhras et al [48], the multiquadric radial basis function method (RBFs) based on a finite point formulation and HSDT by Ferreira et al [49], the closed form solution based on a trigonometric shear deformation theory (TrSDT) by Mantari et al [50], the closed form solution based on an exponential shear deformation theory (ESDT) by Karama et al [51], the IGA based on the dTrSDTs [38,39,7] and an exact 3D elasticity approach studied by Pagano [47]. Table 3 is provided the comparison between the present method and other methods.…”

“…The normalized displacement and stresses of a square plate are defined as: Table 4 lists the results of the IGA based on present theory using 17 × 17 cubic B-Spline elements. Numerical solutions are compared to those reported in the literature such as the closed form solution based on HSDT by Reddy [6], the closed form solution based on ESDT by Karama et al [51], the closed form solution based on TrSDT by Mantari et al [50], the closed form solution based on inverse hyperbolic shear deformation theory (IHSDT) by Grover et al [52], the IGA solution based on the dTrSDTs [38,7] and an exact elasticity solution by Pagano [47]. The obtained results indicate a reasonably good agreement with other available ones for all a/h ratios.…”

On the use of finite strip method for buckling analysis of moderately thick plate by refined plate theory and using new types of functions

“…Although the FSDT provides a sufficiently accurate description of response for thin to moderately-thick plates, it is not convenient to use due to the difficulty of determining an accurate shear correction factor. Thus, to avoid the use of a shear correction factor, many higher-order shear deformation plate theories (HSDTs) were proposed, including the theories of Reddy (1984); Ambartsumian (1958); Levinson (1980); Murthy (1981); Kaczkowski (1968); Panc (1975); Karama et al (2009Karama et al ( , 2003; ; Zenkour (2005); ; Touratier (1991); Benyoucef et al (2010); Atmane et al (2010); Soldatos (1992). Although the HSDTs with five unknowns provided sufficiently accurate results for thin to thick plate, their equations of motion were more complicated than those of the FSDT and CPT.…”