Modeling And Analysis Of Curvilinearly Stiffened Plates And Shells

In order to study the static and dynamic characteristics of the curvilinearly stiffenedplates and shells, their theoretical models are built, and the corresponding efficient analysismethods are developed. The accuracy verification is performed by a great number ofnumerical examples. This thesis mainly contains following parts:1) The theoretical models and characteristics of the stiffened plates and shells arebriefly reviewed. The theories of beams, plates and shells are introduced. The developmentof research on the static, vibration and buckling analysis of stiffened plates and shells arepresented in detail. The concept of curvilinearly stiffened plates and shells and its researchbackground are introduced. Also, the research contents of this thesis are presented insummary.2) A finite element method based approach is developed for studying the static,vibration and buckling behavior of curvilinearly stiffened plates in the presence of in-planecompressive and tensile stresses. The first order shear deformation theory (FSDT) isemployed for both the plate and the Timoshenko beam modeling. Interpolation functionsare used to build the displacement mapping between the stiffener and the plate nodes toallow the stiffener to be placed anywhere within the plate. One of the advantages of thepresent method is that the plate need not be re-meshed while the stiffener configuration ischanged, and second, results obtained by the present method with much fewer number ofelements match well with the results obtained by using a commercial FEM software.Several numerical examples are solved to study both the static and dynamic behaviors ofstiffened plates. The effects of boundary conditions, stiffener eccentricity, stiffenercurvature, stiffener-plate geometry parameters, in-plane load condition, stiffener-platecross-section area ratio and stiffness ratio on the static and dynamic behaviors ofcurvilinearly stiffened plate are investigated. Results have shown that behavior of thenatural frequency parameter as a function of applied in-plane stress could be affected by theplate thickness, in-plane load condition, stiffener-plate cross-section area ratio and stiffnessratio during compression only, but not when subjected to in-plane tension.3) Based on the von Karman’s large deformation theory, the large deformation and thelarge amplitude vibration of the curvilinearly stiffened plates are analyzed. The secantstiffness matrix of the curvilinearly stiffened plates is derived, including the consideration of the geometrically nonlinear effect of the curvilinear stiffener. Similarly, the stiffener canbe placed anywhere within the plate elements. Results obtained by the present method withmuch fewer number of elements match well with the results obtained by using acommercial FEM software and the refercences.4) The free vibration of curvilinearly stiffened shallow shells is investigated by theRitz method. Based on the first order shear deformation shell theory and3-D curved beamtheory, the strain and kinetic energies of the stiffened shells are introduced. The stiffenercan be placed anywhere within the shell. Numerical results with different geometrical shellsand boundary conditions, and different stiffener locations and curvatures are analyzed toverify the feasibility of the presented Ritz method for solving the problems. The resultsshow good agreement with those using other methods, e.g., using a converged set of resultsobtained by Nastran.5) The free vibration of curvilinearly stiffened cylindrical shells is studied by using thefinite element method. The first order shear deformation theory (FSDT) is employed forboth the shell and the Timoshenko beam modeling. The stiffener is assumed to beperpendicular to the shell. A local coordinate system consisting with the tangential,geodesic and normal directions is introduced to model the stiffener. Interpolationfunctions are used to build the displacement mapping between the stiffener and the shellnodes to allow the stiffener to be placed anywhere within the shell. Numerical examplesshow that the present FE method can obtain sufficiently precise results with a lesser numberof elements as compared to the commercial software Nastran.In conclusion, the static and dynamic characteristics of the curvilinearly stiffenedplates and shells are modeled and analyzed. In this thesis, first, the stiffener can be placedanywhere within the plate/shell, so that the plate/shell need not to be re-meshed andre-computed while the stiffener configuration is changed; and second, compared to acommercial software such as Nastran, using a fewer degrees of freedom yield sufficientlyresults. They are the advantages of the present methods, and they can be beneficial forperforming optimization studies in the future work.