Application of the variational-asymptotical method to laminated composite plates
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Hodges, Dewey H.↗
Engineering topics
Atilgan, Ali R.
Publications and source records attributed to Atilgan, Ali R..
Application of the variational-asymptotical method to composite plates
A method is developed for the 3D analysis of laminated plate deformation which is an extension of a variational-asymptotical method by Atilgan and Hodges (1991). Both methods are based on the treatment of plate deformation by splitting the 3D analysis into linear through-the-thickness analysis and 2D plate analysis. Whereas the first technique tackles transverse shear deformation in the second asymptotical approximation, the present method simplifies its treatment and restricts it to the first approximation. Both analytical techniques are applied to the linear cylindrical bending problem, and the strain and stress distributions are derived and compared with those of the exact solution. The present theory provides more accurate results than those of the classical laminated-plate theory for the transverse displacement of 2-, 3-, and 4-layer cross-ply laminated plates. The method can give reliable estimates of the in-plane strain and displacement distributions.
Hodges, Dewey H.↗
A geometrically nonlinear theory of elastic plates
A set of kinematic and intrinsic equilibrium equations is derived for plates undergoing large deflection and rotation but with small strain. The large rotation is treated by the general finite rotation of a frame in which the material points that are originally along a normal line in the undeformed plate undergo only small displacements. Exact intrinsic virtual strain-displacement relations are derived; using a reduced 2-D strain energy function from which the warping has been systematically eliminated, a set of intrinsic equilibrium equations follows. It is demonstrated that only five equilibrium equations can be derived in this way, because the component of virtual rotation about the normal is not independent. These equations include terms which cannot be obtained without the use of a finite rotation vector which contains three nonzero components. These extra terms correspond to the difference of in-plane shear stress resultants in other theories.
Hodges, Dewey H.↗
Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections
A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.
Atilgan, Ali R.↗
On the strain energy of laminated composite plates
The present effort to obtain the asymptotically correct form of the strain energy in inhomogeneous laminated composite plates proceeds from the geometrically nonlinear elastic theory-based three-dimensional strain energy by decomposing the nonlinear three-dimensional problem into a linear, through-the-thickness analysis and a nonlinear, two-dimensional analysis analyzing plate formation. Attention is given to the case in which each lamina exhibits material symmetry about its middle surface, deriving closed-form analytical expressions for the plate elastic constants and the displacement and strain distributions through the plate's thickness. Despite the simplicity of the plate strain energy's form, there are no restrictions on the magnitudes of displacement and rotation measures.
Atilgan, Ali R.↗
New, unusual and nonclassical behavior of thin-walled composite structures
Examples are discussed which illustrated several new, unusual, and nonclassical effects that are present in thin-walled composite structures. Some of the unusual deformation characteristics occur naturally, such as the apparent increased flexibility of thin-walled beam structures due to bending-transverse shear and extension-transverse shear elastic couplings. Others are created intentionally, such as the exaggerated Poisson expansion in the tailored wing covers that produces elastic chordwise camber deformations.
Rehfield, Lawrence W.↗
Limitations and improvements of one-dimensional beam dynamics
The static and dynamic behavior limitations of 1D beam modeling are discussed, with a view to the prediction of high frequency vibrations. A methodology is suggested whereby the construction of 3D dispersion curves is followed by the incorporation of asymptotical considerations to calculate the lowest high-frequency branches of the long-wave vibrations, as well as some short-wave vibrations. A comparison of the two will then yield the constraints for the one-dimensional composite beam modeling of both dynamic and static applications.
Atilgan, Ali R.↗
Modeling of composite beams and plates for static and dynamic analysis
A rigorous theory and corresponding computational algorithms was developed for a variety of problems regarding the analysis of composite beams and plates. The modeling approach is intended to be applicable to both static and dynamic analysis of generally anisotropic, nonhomogeneous beams and plates. Development of a theory for analysis of the local deformation of plates was the major focus. Some work was performed on global deformation of beams. Because of the strong parallel between beams and plates, the two were treated together as thin bodies, especially in cases where it will clarify the meaning of certain terminology and the motivation behind certain mathematical operations.
Hodges, Dewey H.↗
Analysis, design and elastic tailoring of composite rotor blades
The development of structural models for composite rotor blades is summarized. The models are intended for use in design analysis for the purpose of exploring the potential of elastic tailoring. The research was performed at the Center for Rotary Wing Aircraft Technology.
Rehfield, Lawrence W.↗
A structural model for composite rotor blades and lifting surfaces
Composite material systems are currently candidates for aerospace structures, primarily for the design flexibiity they offer i.e., it is possible to tailor the material and manufacturing approach to the application. Two notable examples are the wing of the Grumman/USAF/DARPA X-29 and rotor blades under development by the U.S.A. Aerostructures Directorate (AVSCOM), Langley Research Center. A working definition of elastic or structural tailoring is the use of structural concept, fiber orientation, ply stacking sequence, and a blend of materials to achieve specific performance goals. In the design process, choices of materials and dimensions are made which produce specific response characteristics which permit the selected goals to be achieved. Common choices for tailoring goals are preventing instabilities or vibration resonances or enhancing damage tolerance. An essential, enabling factor in the design of tailored composite structures is structural modeling that accurately, but simply, characterizes response. The objective of this paper is to improve the single-cell beam model for composite rotor blades or lifting surfaces and to demonstrate its usefullness in applications.
Rehfield, Lawrence W.↗
Structural modeling for multicell composite rotor blades
Composite material systems are currently good candidates for aerospace structures, primarily for the design flexibility they offer, i.e., it is possible to tailor the material and manufacturing approach to the application. A working definition of elastic or structural tailoring is the use of structural concept, fiber orientation, ply stacking sequence, and a blend of materials to achieve specific performance goals. In the design process, choices of materials and dimensions are made which produce specific response characteristics, and which permit the selected goals to be achieved. Common choices for tailoring goals are preventing instabilities or vibration resonances or enhancing damage tolerance. An essential, enabling factor in the design of tailored composite structures is structural modeling that accurately, but simply, characterizes response. The objective of this paper is to present a new multicell beam model for composite rotor blades and to validate predictions based on the new model by comparison with a finite element simulation in three benchmark static load cases.
Rehfield, Lawrence W.↗