Vibration and Buckling Analysis of Unitized Structure Using Meshfree Method and Kriging Model

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Virginia Tech


The Element Free Galerkin (EFG) method, which is based on the Moving Least Squares (MLS) approximation, is developed here for vibration, buckling and static analysis of homogenous and FGM plate with curvilinear stiffeners. Numerical results for different stiffeners configurations and boundary conditions are presented. All results are verified using the commercial finite element software ANSYS® and other available results in literature.

In addition, the vibration analysis of plates with curvilinear stiffeners is carried out using Ritz method. A 24 by 28 in. curvilinear stiffened panel was machined from 2219-T851 aluminum for experimental validation of the Ritz and meshfree methods of vibration mode shape predictions. Results were obtained for this panel mounted vertically to a steel clamping bracket using acoustic excitation and a laser vibrometer. Experimental results appear to correlate well with the meshfree and Ritz method results.

In reality, many engineering structures are subjected to random pressure loads in nature and cannot be assumed to be deterministic. Typical engineering structures include buildings and towers, offshore structures, vehicles and ships, are subjected to random pressure. The vibrations induced from gust loads, engine noise, and other auxiliary electrical system can also produce noise inside aircraft. Consequently, all flight vehicles operate in random vibration environment. These random loads can be modeled by using their statistical properties. The dynamical responses of the structures which are subjected to random excitations are very complicated. To investigate their dynamic responses under random loads, the meshfree method is developed for random vibration analysis of curvilinearly-stiffened plates.

Since extensive efforts have been devoted to study the buckling and vibration analysis of stiffened panel to maximize their natural frequencies and critical buckling loads, these structures are subjected to in-plane loading while the vibration analysis is considered. In these cases the natural frequencies calculated by neglecting the in-plane compression are usually over predicted. In order to have more accurate results it might be necessary to take into account the effects of in-plane load since it can change the natural frequency of plate considerably. To provide a better view of the free vibration behavior of the plate with curvilinear stiffeners subjected to axial/biaxial or shear stresses several numerical examples are studied.

The FEM analysis of curvilinearly stiffened plate is quite computationally expensive, and the meshfree method seems to be a proper substitution to reduce the CPU time. However it will still require many simulations. Because of the number of simulations may be required in the solution of an engineering optimization problem, many researchers have tried to find approaches and techniques in optimization which can reduce the number of function evaluations. In these problems, surrogate models for analysis and optimization can be very efficient. The basic idea in surrogate model is to reduce computational cost and giving a better understanding of the influence of the design variables on the different objectives and constrains. To use the advantage of both meshfree method and surrogate model in reducing CPU time, the meshfree method is used to generate the sample points and combination of Kriging (a surrogate model) and Genetic Algorithms is used for design of curvilinearly stiffened plate. The meshfree and kriging results and CPU time were compared with those obtained using EBF3PanelOpt.



Random vibration, Curvilinear stiffener, Stiffened plate, Functionally Graded Material, Optimization, Meshfree, Element Free Galerkin, Surrogate model, Kriging, Buckling, Vibration