Ali Yeilaghi Tamijani

Buckling and Static Analysis of Curvilinearly Stiffened Plates Using Mesh-Free Method

With the advancement s being made in manufactu ring technology, it is now possible to manufacture panels with arbitrary curvilinear stiffeners. A plate with curvilinear stiffener s can in some cases yield a desired structural response but with a lower mass . In this paper , the Element Free Galerkin (EFG) method is employed for buckling and static analysis of stiffened plates. The formulation allows the placeme nt of any number of arbitrarily curvilinear stiffeners within a plate. The First Order Shear Deformation Theory (FSDT) is used to model the behav ior of the plate and the stiffener . Moving Least Squares (MLS) approximation is used to construct the shape function s. One of the major difficulties in the implementation of some mesh free methods is the imposition of essential boundary conditions as the appro ximations do not pass through the nodal parameter values. In this research , the penalty method is used for satisfying the boundary conditions. Using a meshfree method sets free the user from providing a nodal line on the plate along every stiffener. This i s very beneficial for performing optimization studies. Several numerical examples using both straight and curvilinear stiffener s are obtained and compared with those available in the literature and those obtained using ANSYS ® . This demonstrate s the validit y of th e presented approach .

Vibration of Plate with Curvilinear Stiffeners Using Mesh-Free Method

The element-free Galerkin method, which is based on the moving-least-squares approximation, is developed for vibration analysis of unitized structures (e.g., a plate with curvilinear stiffeners). The plate and stiffeners are modeled using the first-order shear deformation theory and Timoshenko beam theory, respectively. The moving-least-squares approximation does not satisfy the delta function property. Consequently, an approximation method (e.g., the well-known penalty method) must be used for imposing essential boundary conditions. A key benefit of using element-free Galerkin for the vibration analysis of a stiffened panel is that the locations and curvatures of the stiffeners can be changed without modifying the plate nodes. Numerical results for different stiffeners, configurations, and boundary conditions are presented. All results are verified using the commercial finite-element software ANSYS. Excellent agreement is seen in all cases. A comparison of the present formulations with other available results for stiffened plates is also made. The mesh-free approach yields highly accurate results for the plates with curvilinear stiffeners.

Multidisciplinary Optimization of Supersonic Wing Structures Using Curvilinear Spars and Ribs (SpaRibs)

The optimization of supersonic aircraft structures needs to address different aspects of the design as the internal structural layout, the sizing of the structural components, the aerodynamic loads developed for the given flight conditions and the aeroelastic response of the structure. In particular, the study of the interaction between the structure and the aerodynamics is critical for designing large supersonic transport aircraft and must be considered in an optimization framework which aims to obtain more efficient wing structures. In this paper, the SpaRibs design concept is implemented in a multidisciplinary optimization framework including structures, static aerodynamics and flutter analysis, in an effort to reduce the weight of a baseline supersonic transport aircraft, given structural and aerodynamic/aeroelastic constraints for given flight conditions. The framework incorporates global optimization and local optimization loops which are executed following a two-step optimization process and interact in a synergetic manner for the efficient computation of the responses required by the design process. The main purpose of the global optimization loop is to optimize the internal structural layout using the SpaRibs. In other words, the topology of the wing is changed during the global optimization. However, the responses computed depend also on the size of the structural components and not only on the layout. In particular, the

Chebyshev-Ritz Approach to Buckling and Vibration of Curvilinearly Stiffened Plate

loading,increasingfromzerotothebucklingload,onthenaturalfrequenciesisstudied.Severalnumericalexamples are compared with the other results available in the literature and mesh free results, illustrating the accuracy of the present approach. This paper also shows that the in-plane load can lead to a significant change in the natural frequency and also in some cases the corresponding mode shapes of plates with curvilinear stiffeners. Numerical results are presented for a range of plate aspect ratios, bending the stiffness ratios of the stiffener to that of the plate andthearearatiosofthestiffenertothatoftheplate.Theeffectoftheseparametersonthenaturalfrequenciesofthe plate with a different number of curvilinear stiffeners under in-plane loads is studied. For studying the influence of thein-planeloadonnaturalfrequency,bothaxial/biaxialandshearin-planeloadsareconsidered.Numericalresults show that the vibration behavior of the stiffened plate in the presence of in-plane loads is influenced by different parameters, such as the plate aspect ratio, the stiffener area ratio, the stiffener stiffness ratio, and the number of stiffeners in the panel.

Free Vibration Analysis of Curvilinear-Stiffened Plates and Experimental Validation

In this research, the vibration analysis of plates with curvilinear stiffeners is carried out. The Ritz method is applied while stiffeners are considered as discrete elements. The first-order shear deformation theory is used to represent the plate and stiffener. Chebyshev polynomial functions are used as the basic functions in the Ritz method. The major part of this work is concerned with modeling the curvilinear stiffeners and comparing the results with experimental data. By considering the curvilinear stiffeners, the curvature, the continuous variation in orientation, can be used in controlling different mode shapes in addition to the associated frequencies. It can provide a mechanism to passively control the dynamic response under certain excitations. In the present method, the geometric properties of curvilinear stiffeners can be modified without changing the plate geometric properties. In the developed formulations, both eccentric and concentric stiffeners were studied. Natural frequencies for plates with straight stiffeners were compared with the results available in the literature. A good agreement was seen. A 24 by 28 in. curvilinear-stiffened panel was machined from 2219-T851 aluminum for experimental validation of the Ritz and meshfree method 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 theoretical predictions.

Vibration Analysis of Curvilinearly-Stiffened Functionally Graded Plate Using Element Free Galerkin Method

The element free Galerkin (EFG) method is developed for the free vibration of a functionally-graded plate with curvilinear stiffeners. The governing equations for the plate and stiffeners are derived by using the first order shear deformation theory. The in-plane deformation, transverse deflection and rotations of the plate and stiffener are expressed using moving least square (MLS) approximation. The penalty method is used to impose the boundary conditions. Material properties of the plate are assumed to vary continuously through the thickness, according to a power law, in terms of the volume fractions of the constituents. The formulation can model stiffeners having arbitrary orientation, curvature, and eccentricity. Several numerical examples for various material compositions and boundary conditions are compared with the other results available in the literature, illustrating the accuracy of the present approach. Finally, the influences of material composition, stiffeners number, and size on natural frequency is investigated.

Random Response Analysis of Curvilinearly Stiffened Plates Using Element-Free Galerkin Method

An Element Free Galerkin (EFG) formulation is presented for studying the random response of curvilinearly-stiffened plates. The structure is subjected to stationary random stochastic loading. The random loads are assumed as stationary in time but can be nonhomogeneous in space. The spectral density of the nodal force vector is formulated using the displacement shape functions. The direct complex matrix inversion method and modal superposition method are used to obtain the random response of structure. The spectral density of displacement for un-stiffened plate under white noise and plate with straight stiffeners subjected to jet noise are compared with those available in the literature. The power spectral density of displacement of curvilinearly-stiffened plate under white noise is also verified using the commercial finite element software ANSYS. Excellent agreement is seen in all cases. The effect of stiffener stiffness and curvature and in-plane load on spectral density of deflection of curvilinearly-stiffened plate is also investigated.

Buckling and Vibration of Curvilinearly-Stiffened Plate Subjected to In-Plane Loads Using Chebyshev Ritz Method1

In this research, the free vibration of plates with curvilinear stiffeners subjected to inplane loading is studied. The First Order Shear Deformation Theory (FSDT) is used to model both the plate and stiffeners. The transverse deflection and rotations of the plate and stiffener are expressed in terms of Chebyshev polynomials. The stiffness and geometric stiffness matrices of the curvilinearly-stiffened plate are obtained by superimposing the strain energy and potential of the membrane force for both the curvilinear stiffeners and the plate. Results are computed for unstiffened and stiffened plate with straight and curvilinear stiffeners using different boundary conditions. The effect of in-plane loading, increasing from zero to the buckling load, on the natural frequencies is studied. The formulation can model stiffeners having arbitrary orientation, curvature and eccentricity. Several numerical examples are compared with the other results available in the literature and meshfree results, illustrating the accuracy of the present approach. This paper also shows that the inplane load can lead to a significant change in the natural frequency and also in some cases the corresponding mode shapes of plate with curvilinear stiffeners. Numerical results are presented for a range of plate aspect ratios, bending stiffness ratios of the stiffener to that of the plate and area ratios of the stiffener to that of the plate. The effect of these parameters on the natural frequencies of the plate with different number of curvilinear stiffeners under in-plane loads is studied. For studying the influence of the in-plane load on natural frequency, both axial/biaxial and shear in-plane loads are considered. Numerical results

Flutter Analysis of Laminated Curvilinear-Stiffened Plates

This paper proposes the use of curvilinear stiffeners as a mechanism to control supersonic panel flutter. To account for transverse shear deformation, the plate and stiffeners are modeled according to the first-order shear deformation theory and Timoshenko beam theory, respectively. The Chebyshev polynomials are the basis of the deflection and rotation functions in the Ritz method. The aeroelastic load is formulated according to the first-order high-Mach-number approximation to linear potential flow theory. The minimum potential energy and Hamilton’s principle are used to solve the problem. Plots of frequency versus aerodynamic pressure and damping versus aerodynamic pressure are used to determine the critical aerodynamic pressure, and hence to predict flutter of various isotropic and composite, stiffened, and unstiffened plates. The results for the flutter of straight-stiffened plates are validated through comparison with published papers. Several numerical examples are discussed, for which parametric st...

Preliminary Wing Study of General Aviation Aircraft with Stitched Composite Panels

A new approach in the design of aerospace vehicles was recently introduced by NASA and Boeing researchers to meet the new challenges in aviation. This innovative configuration is called pultruded rod stitched efficient unitized structure, a stitched carbon–epoxy material system that offers the opportunity for designing stiffer, lower weight, and more cost-efficient aircraft by eliminating fasteners and incorporating damage-tolerance concepts. Aside from superior structural performance and low-cost manufacturing methods, this configuration must also demonstrate advanced aeroelastic behavior to be fully implemented in commercial aircraft. A preliminary wing study of a general aviation aircraft that embodies pultruded rod stitched efficient unitized structure technology is presented in this paper, which will be compared with the structural, dynamic, and aeroelastic behavior of the original metallic wing model. The study showed that the presence of pultruded rod stitched efficient unitized structure panels le...