Large deflection analysis of laminated composite plates using layerwise displacement model
Апстракт
In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer d...ependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.
Кључне речи:
geometrically nonlinear analysis / composite plates / continuum finite elementИзвор:
Structural Engineering and Mechanics, 2011, 40, 2, 257-277Колекције
Институција/група
GraFarTY - JOUR AU - Ćetković, Marina AU - Vuksanović, Đorđe PY - 2011 UR - https://grafar.grf.bg.ac.rs/handle/123456789/347 AB - In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers. T2 - Structural Engineering and Mechanics T1 - Large deflection analysis of laminated composite plates using layerwise displacement model EP - 277 IS - 2 SP - 257 VL - 40 UR - https://hdl.handle.net/21.15107/rcub_grafar_347 ER -
@article{ author = "Ćetković, Marina and Vuksanović, Đorđe", year = "2011", abstract = "In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.", journal = "Structural Engineering and Mechanics", title = "Large deflection analysis of laminated composite plates using layerwise displacement model", pages = "277-257", number = "2", volume = "40", url = "https://hdl.handle.net/21.15107/rcub_grafar_347" }
Ćetković, M.,& Vuksanović, Đ.. (2011). Large deflection analysis of laminated composite plates using layerwise displacement model. in Structural Engineering and Mechanics, 40(2), 257-277. https://hdl.handle.net/21.15107/rcub_grafar_347
Ćetković M, Vuksanović Đ. Large deflection analysis of laminated composite plates using layerwise displacement model. in Structural Engineering and Mechanics. 2011;40(2):257-277. https://hdl.handle.net/21.15107/rcub_grafar_347 .
Ćetković, Marina, Vuksanović, Đorđe, "Large deflection analysis of laminated composite plates using layerwise displacement model" in Structural Engineering and Mechanics, 40, no. 2 (2011):257-277, https://hdl.handle.net/21.15107/rcub_grafar_347 .