High-Efficiency Dynamic Modeling of a Helical Spring Element Based on the Geometrically Exact Beam Theory

This paper presents a modeling study of the dynamics of a helical spring element with variable pitch and radius considering both the static stiffness and dynamic response by using the geometrically exact beam theory. The geometrically exact beam theory based on the Euler–Bernoulli beam hypothesis is described, of which the shear deformations are ignored. Unlike the traditional spliced curved beam element method, the helical spring element is described with curvature vector and axial strain by establishing and spline-interpolating a function of the radius, the height, the polar angle, and the torsion angle of the whole spring. In addition, a model smoothing method is developed and applied in the numerical analysis to filter the high-frequency oscillation component of the flexible multibody systems, so as to correct the system dynamic equations and improve the calculation efficiency when solving the static equilibrium of the spring. This study also carries out five numerical trials to validate the above dynamic procedure of the helical spring element. The example of the spring static stiffness design shows that the proposed helical spring procedure enables one to deal with practical engineering applications.

Dynamic Analysis of Spatial Truss Structures Including Sliding Joint Based on the Geometrically Exact Beam Theory and Isogeometric Analysis

With increasing of the size of spatial truss structures, the beam component will be subjected to the overall motion with large deformation. Based on the local frame approach and the geometrically exact beam theory, a beam finite element, which can effectively reduce the rotational nonlinearity and is appropriate for finite motion and deformation issues, is developed. Dynamic equations are derived in the Lie group framework. To obtain the symmetric Jacobian matrix of internal forces, the linearization operation is conducted based on the previously converged configuration. The iteration matrix corresponding to the rotational parameters, including the Jacobian matrix of inertial and internal forces in the initial configuration, can be maintained in the simulation, which drastically improves the computational efficiency. Based on the Lagrangian multiplier method, the constraint equation and its Jacobian matrix of sliding joint are derived. Furthermore, the isogeometric analysis (IGA) based on the non-uniform rational B-splines (NURBS) basis functions, is adopted to interpolate the displacement and rotation fields separately. Finally, three dynamic numerical examples including a deployment dynamic analysis of spatial truss structure are conducted to verify the availability and the applicability of the proposed formulation.

Aeroelastic Response Analysis of Composite Blades Based on Geometrically Exact Beam Theory

The geometrically exact nonlinear beam theory consisting of the latest version of two-dimensional variational asymptotic beam sectional analysis (VABS) and one-dimensional geometrically exact beam theory (GEBT) has been widely used for the structural analysis of composite beam structures. The theory can be used for establishing the aeroelastic model of composite blades undergoing large deflections to improve computational accuracy and efficiency. In this paper, the theory has been extended from structural analysis to aeroelastic analysis of blade, and an accurate and efficient method for aeroelastic response analysis of composite blades has been presented based on the theory and unsteady aerodynamic model. The geometrically exact nonlinear equations of motion and the latest VABS are used to deal with one-dimensional beam analysis and the structural property of blade cross section, respectively. The Peters–He finite state dynamic wake model and the Peters finite state airloads theory are used to calculate the induced velocity and blade airloads, respectively. The presented method has been used to analyze the aeroelastic responses of composite blades, and its accuracy has been verified by experimental data. The influence of transverse shear deformation on the aeroelastic response of composite blades was also investigated, indicating that the transverse shear deformation has a nonnegligible effect on aeroelastic response analysis of hingeless composite rotors in hover.

Structural Dynamic Analysis of a Tidal Current Turbine Using Geometrically Exact Beam Theory

This paper presents a numerical study of the dynamic performance of a vertical axis tidal current turbine. First, we introduce the geometrically exact beam theory along with its numerical implementation the geometric exact beam theory (GEBT), which are used for structural modeling. We also briefly review the variational-asymptotic beam sectional analysis (VABS) theory and discrete vortex method with free-wake structure (DVM-UBC), which provide the one-dimensional (1D) constitutive model for the beam structures and the hydrodynamic forces, respectively. Then, we validate the current model with results obtained by ANSYS using three-dimensional (3D) solid elements and good agreements are observed. We investigate the dynamic performance of the tidal current turbine including modal behavior and transient dynamic performance under hydrodynamic loads. Finally, based on the results in the global dynamic analysis, we study the local stress distributions at the joint between blade and arm by VABS. It is concluded that the proposed analysis method is accurate and efficient for tidal current turbine and has a potential for future applications to those made of composite materials.

Ultimate strength of steel beam-columns under axial compression

This article presents a semi-analytical method to calculate the ultimate strength of inelastic beam-columns with I-shaped cross section using geometrically exact beam theory. A computer code based on this method has been applied to beam-columns under axial compression. The results agree with nonlinear finite element analysis. Compared with previous step-by-step integration approach, this new method is more efficient and can be extended to multi-span beam-columns and other load combinations including lateral pressure. The presented beam-column model is ideally suited for ultimate strength prediction of stiffened steel panels of ships and offshore structures.

On the Compatibility Equations in Geometrically Exact Beam Finite Element

This paper discusses the compatibility equations which relate the velocity field and the strain field in geometrically exact beam theory. The analysis is carried out in the context of intrinsic equations, namely the dynamic equilibrium equations are formulated in terms of local velocities and strains only. In addition to the well established objectivity and path-independence requirements of the spatial discretization, these compatibility equations show that a consistent spatial interpolation of the velocity field should depend on the curvature of the beam, including initial curvature and curvature from the deformation, and it is shown that this consistency is connected to the ability of the finite element to represent exactly rigid body motion velocities. A two node interpolation scheme is studied and it appears that, as the element gets smaller under mesh refinement, the effect of this dependency reduces, leading eventually to the classical linear shape functions.