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Abstract
This paper is concerned with the bending of laminated composite plates with arbitrary lay-up and general boundary conditions. The analysis is based on the small deflection, first-order shear deformation theory of composite plates, which utilizes the Reissner-Mindlin plate theory. In solving the aforementioned plate problems, a general algorithm based on the Ritz method and the use of beam orthogonal polynomials as coordinate functions is derived. This general algorithm provides an analytical approximate solution that can be applied to the static analysis of moderately thick laminated composite plates with any lamination scheme and combination of edge conditions. The convergence, accuracy, and flexibility of the obtained general algorithm are shown by computing several numerical examples and comparing some of them with results given in the literature. Some results, including general laminates and nonsymmetrical boundary conditions with free edges, are also presented.
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References
- Bhat RB (1985), Plate deflection using orthogonal polynomials. Journal of Engineering Mechanics 111:1301-1309.
- Bodaghi M, Saidi AR (2010), Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory. Applied Mathematical Modeling 34:3659-3673.
- Daghia F, Miranda de S, Ubertini F, Viola E (2008), A hybrid stress approach for laminated composite plates within the first-order shear deformation theory. International Journal of Solids and Structures 45:1766-1787.
- Fares ME, Elmarghany M (2008), A refined zigzag nonlinear first-order shear deformation theory of composite laminated plates. Composite Structures 82:71-83.
- Khdeir AA, Reddy JN (1989), Exact solutions for the transient response of symmetric cross-ply laminates using a higher-order plate theory. Composites Science and Technology 34:205-224.
- Lekhnitskii SG (1968), Anisotropic Plates. New York, USA, Gordon and Breach Science Publishers.
- Liew KM, Han JB, Xiao ZM (1996), Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility. International Journal of Solids and Structures 33:2647-2658.
- Maiti DK, Sinha PK (1996), Bending, free-vibration, and impact response of thick laminated composite plates. Computers and Structures 59:115-129.
- Mindlin RD (1951), Influence rotatory inertia and shear in flexural motion of isotropic, elastic plates. ASME Journal of Applied Mechanics 18:31-38.
- Moleiro F, Mota CM, Mota CA, Reddy JN (2007), Mixed least-squares finite element model for the static analysis of laminated composite plates. Computers & Structures 86:826-838.
- Nallim LG, Grossi RO (2003), On the use of orthogonal polynomials in the study of anisotropic plates. Journal of Sound and Vibration 264:1201-1207.
- Nallim LG, Oller SH, Grossi RO (2005), Statical and dynamical behavior of thin fiber reinforced composite laminates with different shapes. Computer Methods in Applied Mechanics and Engineering 194:1797-1822.
- Nallim LG, Oller SH (2008), An analytical-numerical approach to simulate the dynamic behavior of arbitrarily laminated composite plates. Composite Structures 85:311-325.
- Nguyen VT, Caron JF, Sab K (2005), A model for thick laminates and sandwich plates. Composites Science and Technology 65:475-489.
- Noor AK, Burton WS (1989), Assessment of shear deformation theories for multilayered composite plates. Applied Mechanics Reviews 42:1-13.
- Oktem AS, Chaudhuri RA (2008), Boundary discontinuous Fourier analysis of thick cross-ply clamped plates. Composite Structures 82:539-548.
- Qi Y, Knight NF (1996), A refined first-order sheardeformation theory and its justification by planestrain bending problem of laminated plates. International Journal of Solids and Structures 33:49-64.
- Reddy JN (2003), Mechanics of laminated composite plates and shells: theory and analysis, 2nd ed. Boca Raton, Florida, USA, CRC Press.
- Reissner E (1945), The effect of transverse shear deformation on the bending of elastic plate. ASME Journal of Applied Mechanics 12:69-76.
- Sheikh AH, Haldar S, Sengupta D (2002), A high precision shear deformable element for the analysis of laminated composite plates of different shapes. Composite Structures 55:329-336.
- Tessler A (1993), An improved plate theory of {1,2}- order for thick composite laminates. International Journal of Solids and Structures 30:981-1000.
- Whitney JM (1987), Structural analysis of laminated anisotropic plates. Lancaster, Pennsylvania, USA, Technomic Publishing Company.
- Xiang S, Wang KM, Ai YT, Sha YD, Shi H (2009), Analysis of isotropic, sandwich and laminated plates by a meshless method and various deformation theories. Composite Structures 91:31-37.
- Xiao JR, Gilhooley DF, Batra RC, Gillespie Jr. JW, McCarthy MA (2008), Analysis of thick compos-ite laminates using a higher-order shear and normal deformable plate theory (HOSNDPT) and a meshless method. Composites Part B: Engineering 39:414-427.
References
Bhat RB (1985), Plate deflection using orthogonal polynomials. Journal of Engineering Mechanics 111:1301-1309.
Bodaghi M, Saidi AR (2010), Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory. Applied Mathematical Modeling 34:3659-3673.
Daghia F, Miranda de S, Ubertini F, Viola E (2008), A hybrid stress approach for laminated composite plates within the first-order shear deformation theory. International Journal of Solids and Structures 45:1766-1787.
Fares ME, Elmarghany M (2008), A refined zigzag nonlinear first-order shear deformation theory of composite laminated plates. Composite Structures 82:71-83.
Khdeir AA, Reddy JN (1989), Exact solutions for the transient response of symmetric cross-ply laminates using a higher-order plate theory. Composites Science and Technology 34:205-224.
Lekhnitskii SG (1968), Anisotropic Plates. New York, USA, Gordon and Breach Science Publishers.
Liew KM, Han JB, Xiao ZM (1996), Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility. International Journal of Solids and Structures 33:2647-2658.
Maiti DK, Sinha PK (1996), Bending, free-vibration, and impact response of thick laminated composite plates. Computers and Structures 59:115-129.
Mindlin RD (1951), Influence rotatory inertia and shear in flexural motion of isotropic, elastic plates. ASME Journal of Applied Mechanics 18:31-38.
Moleiro F, Mota CM, Mota CA, Reddy JN (2007), Mixed least-squares finite element model for the static analysis of laminated composite plates. Computers & Structures 86:826-838.
Nallim LG, Grossi RO (2003), On the use of orthogonal polynomials in the study of anisotropic plates. Journal of Sound and Vibration 264:1201-1207.
Nallim LG, Oller SH, Grossi RO (2005), Statical and dynamical behavior of thin fiber reinforced composite laminates with different shapes. Computer Methods in Applied Mechanics and Engineering 194:1797-1822.
Nallim LG, Oller SH (2008), An analytical-numerical approach to simulate the dynamic behavior of arbitrarily laminated composite plates. Composite Structures 85:311-325.
Nguyen VT, Caron JF, Sab K (2005), A model for thick laminates and sandwich plates. Composites Science and Technology 65:475-489.
Noor AK, Burton WS (1989), Assessment of shear deformation theories for multilayered composite plates. Applied Mechanics Reviews 42:1-13.
Oktem AS, Chaudhuri RA (2008), Boundary discontinuous Fourier analysis of thick cross-ply clamped plates. Composite Structures 82:539-548.
Qi Y, Knight NF (1996), A refined first-order sheardeformation theory and its justification by planestrain bending problem of laminated plates. International Journal of Solids and Structures 33:49-64.
Reddy JN (2003), Mechanics of laminated composite plates and shells: theory and analysis, 2nd ed. Boca Raton, Florida, USA, CRC Press.
Reissner E (1945), The effect of transverse shear deformation on the bending of elastic plate. ASME Journal of Applied Mechanics 12:69-76.
Sheikh AH, Haldar S, Sengupta D (2002), A high precision shear deformable element for the analysis of laminated composite plates of different shapes. Composite Structures 55:329-336.
Tessler A (1993), An improved plate theory of {1,2}- order for thick composite laminates. International Journal of Solids and Structures 30:981-1000.
Whitney JM (1987), Structural analysis of laminated anisotropic plates. Lancaster, Pennsylvania, USA, Technomic Publishing Company.
Xiang S, Wang KM, Ai YT, Sha YD, Shi H (2009), Analysis of isotropic, sandwich and laminated plates by a meshless method and various deformation theories. Composite Structures 91:31-37.
Xiao JR, Gilhooley DF, Batra RC, Gillespie Jr. JW, McCarthy MA (2008), Analysis of thick compos-ite laminates using a higher-order shear and normal deformable plate theory (HOSNDPT) and a meshless method. Composites Part B: Engineering 39:414-427.