Slojeviti konačni element za analizu termičke stabilnosti laminatnih kompozitnim ploča

In this paper thermal stability of laminated composite plates is analyzed using layerwise finite element. The weak form of the plate mathematical model is derived using layerwise displacement field of Reddy [1], nonlinear strain-displacement relations (in von Karman sense) and linear orthotropic thermo-mechanical material properties. The weak form is discretized using isoparametric finite element formulation. The nine-node Lagrangian isoparametric element is used to derive element stiffness and geometric stiffness matrix. The originally coded MATLAB program is used to analyze the effects of different boundary conditions on thermo-elastic stability of laminate composite plate. The accuracy of the numerical model is verified by comparison with the available results from the literature

Finite Element Model for the Static Analysis of Laminated Composite and Sandwich Plates

Finite element model for the static analysis of laminated composite and sandwich plates, based on Generalized Laminate Plate Theory (GLPT) is presented in this paper. Within each layer, the theory assumes piece-wise variation of in-plane displacement components, constant transverse displacement component and parabolic distribution of shear stresses, thus accurately modeling the warping of cross section and including the effects of transverse shear deformation. Transverse shear stresses satisfy Hook’s low, 3D equilibrium equations and traction free boundary conditions. Using the assumed displacement field, linear strain-displacement relations and 3D constitutive equations of lamina, equilibrium equations are derived according to the principle of virtual displacements. In the finite element formulation, in-plane displacement components are through the thickness approximated using two-node linear 1D Lagrangian finite element, while the four and nine node 2D Lagrangian elements are used for approximation of displacements in plane. Numerical results for bending stresses, transverse shearing stresses and displacements are presented, showing the parametric effect of plate aspect ratio, side-to-thickness ratio, lamination angle schemes and degree of orthotropy. The accuracy of the results is verified with the 3D elasticity theory, Higher-order Shear Deformation Theory (HSDT), First-order Shear Deformation Theory (FSDT) and Classical Laminated Plate Theory (CLPT) available in the literature. It has been shown that GLPT finite element gives excellent agreement with 3D elasticity theory and may be used in the future linear and nonlinear analysis of laminated composites

Finite Element Model for the Static Analysis of Laminated Composite and Sandwich Plates

Finite element model for the static analysis of laminated composite and sandwich plates, based on Generalized Laminate Plate Theory (GLPT) is presented in this paper. Within each layer, the theory assumes piece-wise variation of in-plane displacement components, constant transverse displacement component and parabolic distribution of shear stresses, thus accurately modeling the warping of cross section and including the effects of transverse shear deformation. Transverse shear stresses satisfy Hook’s low, 3D equilibrium equations and traction free boundary conditions. Using the assumed displacement field, linear strain-displacement relations and 3D constitutive equations of lamina, equilibrium equations are derived according to the principle of virtual displacements. In the finite element formulation, in-plane displacement components are through the thickness approximated using two-node linear 1D Lagrangian finite element, while the four and nine node 2D Lagrangian elements are used for approximation of displacements in plane. Numerical results for bending stresses, transverse shearing stresses and displacements are presented, showing the parametric effect of plate aspect ratio, side-to-thickness ratio, lamination angle schemes and degree of orthotropy. The accuracy of the results is verified with the 3D elasticity theory, Higher-order Shear Deformation Theory (HSDT), First-order Shear Deformation Theory (FSDT) and Classical Laminated Plate Theory (CLPT) available in the literature. It has been shown that GLPT finite element gives excellent agreement with 3D elasticity theory and may be used in the future linear and nonlinear analysis of laminated composites

Finite Element Model of Imperfect Plate in Thermal Environment

In this paper a finite element model for thermal buckling of imperfect plates using Layer Wise (LW) plate mode [1] is presented. The model assumes layerwise variation of in-plane displacements and constant transverse displacement through the thickness of the plate, non-linear strain-displacement relations (in von Karman sense) and linear thermo mechanical material properties. The Koiter model for imperfection is adopted. The Principle of virtual displacements (PVD) is used to derive the weak form of linearized buckling problem. The weak form is discretized using Lagrangian nine-node isoparametric finite element. The original MATLAB program is coded for finite element solution. The effects of imperfection amplitude, imperfection form and plate aspect ratio a/h on critical temperature are analyzed. The accuracy of the numerical model is verified by comparison with the available results from the literature

Finite Element Model of Imperfect Plate in Thermal Environment

In this paper a finite element model for thermal buckling of imperfect plates using Layer Wise (LW) plate mode [1] is presented. The model assumes layerwise variation of in-plane displacements and constant transverse displacement through the thickness of the plate, non-linear strain-displacement relations (in von Karman sense) and linear thermo mechanical material properties. The Koiter model for imperfection is adopted. The Principle of virtual displacements (PVD) is used to derive the weak form of linearized buckling problem. The weak form is discretized using Lagrangian nine-node isoparametric finite element. The original MATLAB program is coded for finite element solution. The effects of imperfection amplitude, imperfection form and plate aspect ratio a/h on critical temperature are analyzed. The accuracy of the numerical model is verified by comparison with the available results from the literature

Slojeviti konačni element za analizu termičke stabilnosti laminatnih kompozitnim ploča

In this paper thermal stability of laminated composite plates is analyzed using layerwise finite element. The weak form of the plate mathematical model is derived using layerwise displacement field of Reddy [1], nonlinear strain-displacement relations (in von Karman sense) and linear orthotropic thermo-mechanical material properties. The weak form is discretized using isoparametric finite element formulation. The nine-node Lagrangian isoparametric element is used to derive element stiffness and geometric stiffness matrix. The originally coded MATLAB program is used to analyze the effects of different boundary conditions on thermo-elastic stability of laminate composite plate. The accuracy of the numerical model is verified by comparison with the available results from the literature

Termička analiza laminatnih kompozitnih i sendvič ploča primenom slojevitog konačnog elementa

In this paper the quasi static response of laminated composite and sandwich plates subjected to lineary varaying through the thickness and sinusoidall distributed in plane temperature field, is analyzed. Mathematical model, based on layer-wise displacement field of Reddy [15], is formulated using small deflection linear-elasticity theory. The principle of virtual displacements (PVD) is used to obtain the weak form of the mathematical model. The weak form is discretized utilizing isoparametric finite element approximation. The originally coded MATLAB program is used to investigate the influence of plate thickness on thermo-elastic response of laminate composite and sandwich plates. The accuracy of the numerical model is verified by comparison with the available results from the literature.U ovom radu analiziran je kvazi statički odgovor laminatnih kompozitnih i sendvič ploča ploča izloženih temperaturnom polju linearno promenlivom po debljini i sinusoiudalno promenlijvom u ravni. Matematički model, zasnovan na slojevitom polju pomeranja koje je predložio Reddy [15], formulisan je koristeći pretpostavke o geometrijskoj, materijalnoj i statičkoj linearnosti problema. Princip virtulanih pomeranja je primenjen za dobijanje slabe forme matematičkog modela. Slaba forma je diskretizovana koristeći izoparametarsku aproksimaciju konačnim elementom. Originalan MATLAB računski program je korišćen za analizu uticaja razlicitih debljina ploče na termo-elastičan odgovor laminatnih kompozitnih i sendvič ploča. Tačnost numeričkog modela je potvrđena poređenjem sa rešenjima iz literature

Free vibrations of laminated composite plates using layerwise displacement model

In this paper Generalized Layer Wise Plate Theory of Reddy (GLPT) is used to formulate an isoparametric finite element model for free vibration of laminated composite plates. With the assumed displacement field, linear strain displacement relations and linear elastic orthotropic material properties for each lamina, virtual work statement is utilized in order to formulate isoparametric finite element model. The original MATLAB computer program is coded for finite element solution. Some new results using GLPT finite element model for soft core sandwich plate is presented, which may be used as the guideline for their optimal design in the laboratory

Vibracije izotropnih, ortotropnih i laminatnih kompozitnih ploča sa različitim graničnim uslovima oslanjanja

In this paper Generalized Layer Wise Plate Theory of Reddy (GLPT) is used to formulate an isoparametric finite element model for free vibrations of isotropic, orthotropic and laminated composite plates. With the assumed displacement field, linear strain displacement relations and linear elastic orthotropic material properties for each lamina, governing differential equations of motion are derived using Hamilton‘s principle. Virtual work statement is then utilized to formulate isoparametric finite element model. The original MATLAB computer program is coded for finite element solution. The parametric effects of plate aspect ratio b / a , side-tothickness ratio a / h , degree of orthotropy 1 2 E / E and boundary conditions on free vibration response of isotropic, orthotropic and anisotropic plates are analyzed. The accuracy of the present formulation is demonstrated through a number of examples and by comparison with results available from the literature.U ovom radu primenom Opšte laminatne teorije ploča (Generalized Layerwise Plate Theory-GLPT), koju je postavio Reddy, formulisan je izoparametarski model konačnog elementa za problem slobodnih vibracija izotropnih, ortotropnih i laminatnih kompozitnih ploča. Osnovne diferencijalne jednačine kretanja izvedene su primenom Hamilton-ovog principa, koristeći pretpostavljeno polje pomeranja, linearne veze deformacija i pomeranja i linearno elastičan ortotropan materijal za svaku od lamina. Princip virtuelnog rada potom je iskorišćen za formulisanje izoparametarskog modela konačnog elementa. Originalni računarski program napisan je za rešenje po Metodi konačnih elemenata, koristeći MATLAB programski jezik. Analiziran je parametarski uticaj odnosa strana ploče , strane prema debljini ploče , stepena ortotropije i graničnih uslova na slobodne vibracije izotropnih, ortotropnih i anizotropnih ploča. Tačnost predstavljene formulacije potvrđena je kroz niz primera i njihovim poređenjem sa rešenjima iz literature

Free vibrations of laminated composite plates using layerwise displacement model

In this paper Generalized Layer Wise Plate Theory of Reddy (GLPT) is used to formulate an isoparametric finite element model for free vibration of laminated composite plates. With the assumed displacement field, linear strain displacement relations and linear elastic orthotropic material properties for each lamina, virtual work statement is utilized in order to formulate isoparametric finite element model. The original MATLAB computer program is coded for finite element solution. Some new results using GLPT finite element model for soft core sandwich plate is presented, which may be used as the guideline for their optimal design in the laboratory