On Timoshenko-like modeling of initially curved and twisted composite beams

The computer program VABS (Variational Asymptotic Beam Section Analysis) uses the variational asymptotic method to split a three-dimensional nonlinear elasticity problem into a twodimensional linear cross-sectional analysis and a one-dimensional, nonlinear beam problem. This is accomplished by taking advantage of certain small parameters inherent to beam-like structures. VABS is able to calculate the one-dimensional cross-sectional stiffness constants, with transverse shear and Vlasov refinements, for initially twisted and curved beams with arbitrary geometry and material properties. Several validation cases are presented. First, an elliptic bar is modeled with transverse shear refinement using the variational asymptotic method, and the solution is shown to be identical to that obtained from the theory of elasticity. The shear center locations calculated by VABS for various cross sections agree well with those obtained from common engineering analyses. Comparisons with other composite beam theories prove that it is unnecessary to introduce ad hoc kinematic assumptions to build an accurate beam model. For numerical validation, values of the one-dimensional variables are extracted from an ABAQUS model and compared with results from a one-dimensional beam analysis using cross-sectional constants from VABS. Furthermore, point-wise three-dimensional stress and strain fields are recovered using VABS, and the correlation with the three-dimensional results from ABAQUS is excellent. Finally, classical theory is shown to be insufficient for general-purpose beam modeling. Appropriate refined theories are recommended for some classes of problems.

Validation of the Variational Asymptotic Beam Sectional Analysis

https://orbit.dtu.dk/files/9784042/Multi_material_topology.pdf

Multi-material topology optimization of laminated composite beam cross sections

Rotating composite beams and blades have a wide range of applications in various engineering structures such as wind turbines, industrial fans, and steam turbines. Therefore, proper understanding of such structures is of a great importance. As a result, the behavior of rotating composite beam structures has received a lot of attention. This paper presents a comprehensive review of scholarly articles about rotating composite beams as published in the past decades. The review addresses analytical, semi-analytical and numerical studies dealing with dynamical problems involving adaptive/smart/intelligent materials (e.g. piezoelectric materials, electrorheological fluids, shape memory alloys, etc.), damping and vibration control, advanced composite materials (e.g. functionally graded materials and nanocomposites), complicating effects and loadings (e.g. added mass, tapered beams, initial curve and twist, etc.), and experimental methods. Moreover, the influence of Vlasov or restrained warping, out-of-plane warping, transverse shear, arbitrary cross-sectional geometry, trapeze phenomena, swept tip, size-dependent effect, as well as other areas that have been considered in research, are reviewed in depth. The review concludes with a presentation of the remaining challenges and future research needs.

Dynamics, vibration and control of rotating composite beams and blades: A critical review

The generalized Timoshenko theory for composite beams embedded in the computer program VABS has the same structure as Timoshenko’s original theory for isotropic beams without the restrictive assumptions of the original theory. An overview of this theory is presented to show its general and rigorous framework. Certain theoretical details missing from previous developments are supplied, such as the proof of a kinematical identity and the expression of the recovery theory in terms of sectional stress resultants. It has been demonstrated that the VABS generalized Timoshenko theory reproduces the elasticity solution for the flexure problem of isotropic prisms. Numerical results are presented in support of the long-term validation effort, focusing especially on calculation of sectional stiffnesses (including shear correction factors) and shear center location, making use of the VABS model for composite beam analysis (including buckling and vibration), and recovering three-dimensional field variables over the section. The accuracy of the VABS generalized Timoshenko theory is demonstrated, and some of its practical advantages over three-dimensional finite element analysis are exhibited. Presented at the 44th Structures, Structural Dynamics and Materials Conference, Norfolk, Virginia, April 7 – 10, 2003 Assistant Professor, Department of Mechanical and Aerospace Engineering, Utah State University, Logan, Utah 84322-4130. Formerly, Post Doctoral Fellow, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia. Email: wenbin.yu@usu.edu. Professor, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia, 303320150. Email: dewey.hodges@ae.gatech.edu. Fellow, AHS.

B. Popescu

Papers

Assessment of beam modeling methods for rotor blade applications