VIBRATIONS OF PRESTRESSED VARIABLE STIFFNESS COMPOSITE AEROSPACE STRUCTURES BY RITZ APPROACH

2021 ◽  
Author(s):  
GIUSEPPE SCIASCIA ◽  
VINCENZO OLIVERI ◽  
PAUL WEAVER
Keyword(s):  
Composite Structures ◽  
Transient Analysis ◽  
Design Space ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Variable Stiffness ◽  
Shell Structures ◽  
Integration Scheme ◽  
Aerospace Structures ◽  
Rational Bézier Surface

With the introduction of the variable stiffness concept, the design space for highperformance lightweight composite structures has expanded significantly. A larger design space, in particular, allows designers to find more effective solutions with higher overall stiffness and fundamental frequency when considering prestressed dynamically excited aerospace components. In this context, an efficient and versatile Ritz method for the transient analysis of prestressed variable stiffness laminated doubly-curved shell structures is presented. The considered theoretical framework is the first-order shear deformation theory without further assumptions on the shallowness or on the thinness of the structure. A rational Bézier surface representation is adopted for the description of the shell allowing general orthogonal surfaces to be represented. General stacking sequences are considered and the unknown displacement field is approximated by Legendre orthogonal polynomials. Stiffened variable angle tow shell structures are modelled as an assembly of shell-like domains and penalty techniques are used to enforce the displacement continuity of the assembled multidomain structure and the kinematical boundary conditions. For the transient analysis of prestressed variable stiffness structures, classical Rayleigh damping is considered and solutions are obtained through the Newmark integration scheme. The proposed approach is validated by comparison with literature and finite elements results and original solutions are presented for prestressed free and forced vibrations of VS stiffened shell structure, proving the ability of the present method in dealing with the analysis of complex aerospace structures.

Ritz Solution for Transient Analysis of Variable-Stiffness Shell Structures

AIAA Journal ◽  
2020 ◽  
Vol 58 (4) ◽  
pp. 1796-1810
Author(s):  
Giuseppe Sciascia ◽  
Vincenzo Oliveri ◽  
Alberto Milazzo ◽  
Paul M. Weaver
Keyword(s):  
Transient Analysis ◽  
Variable Stiffness ◽  
Shell Structures

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

scholarly journals Parametric structural modelling of fish bone active camber morphing aerofoils

2018 ◽  
Vol 29 (9) ◽  
pp. 2008-2026 ◽  
Author(s):  
Andres E Rivero ◽  
Paul M Weaver ◽  
Jonathan E Cooper ◽  
Benjamin KS Woods
Keyword(s):  
Analytical Model ◽  
Composite Laminates ◽  
Plate Theory ◽  
Ritz Method ◽  
Linear Equations ◽  
Variable Stiffness ◽  
Automated Analysis ◽  
Fish Bone ◽  
Two Dimensional ◽  
Wide Range

Camber morphing aerofoils have the potential to significantly improve the efficiency of fixed and rotary wing aircraft by providing significant lift control authority to a wing, at a lower drag penalty than traditional plain flaps. A rapid, mesh-independent and two-dimensional analytical model of the fish bone active camber concept is presented. Existing structural models of this concept are one-dimensional and isotropic and therefore unable to capture either material anisotropy or spanwise variations in loading/deformation. The proposed model addresses these shortcomings by being able to analyse composite laminates and solve for static two-dimensional displacement fields. Kirchhoff–Love plate theory, along with the Rayleigh–Ritz method, are used to capture the complex and variable stiffness nature of the fish bone active camber concept in a single system of linear equations. Results show errors between 0.5% and 8% for static deflections under representative uniform pressure loadings and applied actuation moments (except when transverse shear exists), compared to finite element method. The robustness, mesh-independence and analytical nature of this model, combined with a modular, parameter-driven geometry definition, facilitate a fast and automated analysis of a wide range of fish bone active camber concept configurations. This analytical model is therefore a powerful tool for use in trade studies, fluid–structure interaction and design optimisation.

scholarly journals A Semianalytical Approach for Free Vibration Characteristics of Functionally Graded Spherical Shell Based on First-Order Shear Deformation Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Fuzhen Pang ◽  
Cong Gao ◽  
Jie Cui ◽  
Yi Ren ◽  
Haichao Li ◽  
...  
Keyword(s):  
Free Vibration ◽  
Spherical Shell ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Numerical Verification ◽  
First Order

This paper describes a unified solution to investigate free vibration solutions of functionally graded (FG) spherical shell with general boundary restraints. The analytical model is established based on the first-order shear deformation theory, and the material varies uniformly along the thickness of FG spherical shell which is divided into several sections along the meridian direction. The displacement functions along circumferential and axial direction are, respectively, composed by Fourier series and Jacobi polynomial regardless of boundary restraints. The boundary restraints of FG spherical shell can be easily simulated according to penalty method of spring stiffness technique, and the vibration solutions are obtained by Rayleigh–Ritz method. To verify the reliability and accuracy of the present solutions, the convergence and numerical verification have been conducted about different boundary parameters, Jacobi parameter, etc. The results obtained by the present method closely agree with those obtained from the published literatures, experiments, and finite element method (FEM). The impacts of geometric dimensions and boundary conditions on the vibration characteristics of FG spherical shell structure are also presented.

Predictive analysis of stitched aerospace structures for advanced aircraft

2019 ◽  
Vol 124 (1271) ◽  
pp. 44-54
Author(s):  
B. Horton ◽  
Y. Song ◽  
D. Jegley ◽  
F. Collier ◽  
J. Bayandor
Keyword(s):  
Composite Structures ◽  
Experimental Validation ◽  
Aviation Industry ◽  
Body Structure ◽  
Element Analysis ◽  
Aerospace Structures ◽  
New Approach ◽  
Leading Role ◽  
Modeling Techniques ◽  
Analysis Environment

ABSTRACTIn recent years, the aviation industry has taken a leading role in the integration of composite structures to develop lighter and more fuel efficient aircraft. Among the leading concepts to achieve this goal is the Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) concept. The focus of most PRSEUS studies has been on developing an hybrid wing body structure, with only a few discussing the application of PRSEUS to a tube-wing fuselage structure. Additionally, the majority of investigations for PRSEUS have focused on experimental validation of anticipated benefits rather than developing a methodology to capture the behavior of stitched structure analytically. This paper presents an overview of a numerical methodology capable of accurately describing PRSEUS’ construction and how it may be implemented in a barrel fuselage platform resorting to high-fidelity mesoscale modeling techniques. The methodology benefits from fresh user defined strategies developed in a commercially available finite element analysis environment. It further proposes a new approach for improving the ability to predict deformation in stitched composites, allowing for a better understanding of the intricate behavior and subtleties of stitched aerospace structures.

Structural Analysis of Variable Stiffness Laminated Plates Using First-Order Shear Deformation Theory

2014 ◽  
Author(s):  
A. H. Akbarzadeh ◽  
M. Arian Nik ◽  
D. Pasini
Keyword(s):  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Variable Stiffness ◽  
Buckling Load ◽  
Shear Stresses ◽  
Critical Buckling Load ◽  
First Order ◽  
Stiffness Design ◽  
Transverse Shear Stresses

Constant and variable stiffness strategies have been developed to design a composite laminate. With the former, each layer is designed with straight fibers that have the highest stiffness and strength in the fiber direction. With the latter, on the other hand, the stiffness can change within each layer by placing the fibers along a curvilinear fiber path. A variable stiffness design results in improved structural performance, as well as opens up opportunities to search for trade-off among structural properties. During the manufacture of a variable stiffness design with Automated Fiber Placement, certain defects in the form of gaps and overlaps could appear within the laminate and affect the laminate performance. In this study, we use the first-order shear deformation theory to assess the effect of transverse shear stresses on the critical buckling load, free and forced vibration of a variable stiffness laminate with embedded defects, an issue so far rarely examined in literature. The governing differential equations for the static analysis are first derived. A semi-analytic solution is then obtained using the hybrid Fourier-Galerkin method and the numeric time integration technique. The eigenvalue analysis is also conducted to determine the fundamental frequency and critical buckling load of the plate. It is found that the behavior of a variable stiffness plate is much more affected by the shear stresses than a constant stiffness plate. Ignoring the effect of transverse shear stresses results in 34% error in the predicted buckling load of a variable stiffness laminate with overlaps and a length-to-thickness ratio of 10.

Enhancement to four-node quadrilateral plate elements by using cell-based smoothed strains and higher-order shear deformation theory for nonlinear analysis of composite structures

2018 ◽  
Vol 22 (7) ◽  
pp. 2302-2329
Author(s):  
Lan T That-Hoang ◽  
Hieu Nguyen-Van ◽  
Thanh Chau-Dinh ◽  
Chau Huynh-Van
Keyword(s):  
Nonlinear Analysis ◽  
Shear Deformation ◽  
Composite Structures ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Numerical Results ◽  
Quadrilateral Plate ◽  
Plate Elements ◽  
Strain Smoothing

This paper improves four-node quadrilateral plate elements by using cell-based strain smoothing enhancement and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of composite structures. Small strain-large displacement theory of von Kármán is used in nonlinear formulations of four-node quadrilateral plate elements that have strain components smoothed or averaged over the sub-domains of the elements. From the divergence theory, the displacement gradients in the smoothed strains are transformed from the area integral into the line one. The behavior of composite structures follows the third-order shear deformation theory. The solution of the nonlinear equilibrium equations is obtained by the iterative method of Newton–Raphson with the appropriate convergence criteria. The present numerical results are compared with the other numerical results available in the literature in order to demonstrate the effectiveness of the developed element. These results also contribute a better knowledge and understanding of nonlinear bending behaviors of these composite structures.

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