The paper presents an approach for the formulation of general laminated shells based on a third order shear deformation theory. These shells undergo finite (unlimited in size) rotations and large overall motions but w...The paper presents an approach for the formulation of general laminated shells based on a third order shear deformation theory. These shells undergo finite (unlimited in size) rotations and large overall motions but with small strains. A singularity-free parametrization of the rotation field is adopted. The constitutive equations, derived with respect to laminate curvilinear coordinates, are applicable to shell elements with an arbitrary number of orthotropic layers and where the material principal axes can vary from layer to layer. A careful consideration of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations leads to symmetric tangent stiffness matrices. The matrix formulation adopted here makes it possible to implement the present formulation within the framework of the finite element method as a straightforward task.展开更多
This research work deals with a study on dynamic behavior of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)beams under various types of dynamic loads.Carbon nanotubes(CNTs)are used as the reinforci...This research work deals with a study on dynamic behavior of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)beams under various types of dynamic loads.Carbon nanotubes(CNTs)are used as the reinforcing materials that distribute continuously across the beam thickness.By using third order shear deformable theory(TSDT)in this current study,the straightness and normality of the transverse normal after deformation are unconstrained.The equations of motion based on TSDT are solved by Gram-Schmidt-Ritz method in which the displacement functions are generated via Gram-Schmidt procedure.Additionally,the time-integration of Newmark is also employed to carry out dynamic response of the beams under dynamic loads.Several effects such as material distributions,types of dynamic loads,boundary conditions and so on are taken into account.According to numerical results,it can be revealed that adding small amount of CNTs can reduce considerably the dynamic amplitude of FG-CNTRC beams.Moreover,the dynamic analysis of beam-like structures plays an important role in structural design because mass inertia matrix of the beam being involved in the equations of motion,which yields much larger deflection than that predicted by simple static analysis.展开更多
文摘The paper presents an approach for the formulation of general laminated shells based on a third order shear deformation theory. These shells undergo finite (unlimited in size) rotations and large overall motions but with small strains. A singularity-free parametrization of the rotation field is adopted. The constitutive equations, derived with respect to laminate curvilinear coordinates, are applicable to shell elements with an arbitrary number of orthotropic layers and where the material principal axes can vary from layer to layer. A careful consideration of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations leads to symmetric tangent stiffness matrices. The matrix formulation adopted here makes it possible to implement the present formulation within the framework of the finite element method as a straightforward task.
基金supported by the New Strategic Research(P2P)project(phase 2),Walailak University,Thailand.
文摘This research work deals with a study on dynamic behavior of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)beams under various types of dynamic loads.Carbon nanotubes(CNTs)are used as the reinforcing materials that distribute continuously across the beam thickness.By using third order shear deformable theory(TSDT)in this current study,the straightness and normality of the transverse normal after deformation are unconstrained.The equations of motion based on TSDT are solved by Gram-Schmidt-Ritz method in which the displacement functions are generated via Gram-Schmidt procedure.Additionally,the time-integration of Newmark is also employed to carry out dynamic response of the beams under dynamic loads.Several effects such as material distributions,types of dynamic loads,boundary conditions and so on are taken into account.According to numerical results,it can be revealed that adding small amount of CNTs can reduce considerably the dynamic amplitude of FG-CNTRC beams.Moreover,the dynamic analysis of beam-like structures plays an important role in structural design because mass inertia matrix of the beam being involved in the equations of motion,which yields much larger deflection than that predicted by simple static analysis.
