Omri Rand

Fundamental closed-form solutions for solid and thin-walled composite beams including a complete out-of-plane warping model

A model for predicting the structural behavior of composite beams is presented. The model includes a three-dimensional warping distribution and is designed to handle arbitrary solid cross-sections or general thin-walled geometries. The formulation enables the derivation of fundamental strength-of-materials type closed-form analytic solutions for various basic composite beam configurations and loading modes. These fundamental solutions explicitly identify the origin of the elastic couplings and supply educating insight into the structural mechanisms in composite beams. In addition, the detailed distributions of the out-of-plane warping provided by the present analytic solutions for relatively simple geometries may be used as the basic shear deformation shape functions in numerical analyses of more complex configurations.

Free vibrations of spinning composite cylindrical shells

Abstract The free vibrations of rotating laminated filament-wound cylindrical shells have been investigated. The exact solution procedure was formulated for general field equations and general boundary conditions, arbitrary combinations of lamina materials and fiber orientation. A parametric investigation of the free vibrations spectra has been carried out. The main characteristics of spinning composite shells are presented and discussed as functions of the filament-winding angles, various layups and the rotational velocity.

On the importance of cross-sectional warping in solid composite beams

The relative importance of the cross-sectional warping components in composite beams is studied and demonstrated using an exact solution for solid orthotropic beam of arbitrary cross-sectional geometry that undergoes a bending moment. In light of the effort required for warping modeling in general numerical schemes of composite beams, the present study contributes to the understanding of the importance of modeling the in-plane and the out-of-plane warping components.

Numerical model of the nonlinear behavior of curved rods

Abstract A theoretical model for the nonlinear behavior of curved rods is derived. The model is very general and it allows any combination of geometry, structural properties distribution, load distribution, and boundary conditions. A set of nonlinear equilibrium equations and boundary conditions is obtained. The equations are solved using the Galerkin Method. Two kinds of methods to calculate the cross sectional resultant forces and moments along the rod are described. One method includes differentiation of the displacements along the rod while the other method is based on integration of the loads along the rod. In order to show the use of the model an example is presented. The different nonlinear effects are indicated and discussed.

Free vibration of thin-walled composite blades

Abstract Theoretical analysis for predicting the natural frequencies and mode shapes of rotating thin-walled composite beams is presented. The structural modeling is based on a systematic reduction of a comprehensive structural formulation which contains a detailed description of the out-of-plane warping. The resulting equations describe the dynamics of the axial displacements, two transverse displacements and the twist angle, and are formulated as a standard eigenvalues problem. Coupled modes in symmetric and antisymmetric box-beams are clearly identified and discussed. The results are correlated with other theoretical predictions and provide an additional insight into the vibration characteristics of rotating composite beams.

Nonlinear analysis of orthotropic beams of solid cross-sections

Abstract The paper presents a nonlinear formulation and a finite-differences based numerical solution for the structural behavior of generic orthotropic beams of solid cross-sections. The analysis includes a detailed description of the three-dimensional out-of-plane warping and the solution is achieved by successive iterations while preserving all geometrical nonlinearities. The axial body forces are introduced consistently through the axial differential equilibrium equation. The formulation yields some basic closed-form analytic solutions for homogeneous beams, and the numerical results provide an insight into the coupling effects mechanisms in generic laminated composite beams, including the resulting interlaminar stresses.

Nonlinear analysis of composite thin-walled helicopter blades

Abstract Nonlinear theoretical modeling of laminated thin-walled composite helicopter rotor blades is presented. The derivation is based on nonlinear geometry with a detailed treatment of the body loads in the axial direction which are induced by the rotation. While the in-plane warping is neglected, a three-dimensional generic out-of-plane warping distribution is included. The formulation may also handle varying thicknesses and mass distribution along the cross-sectional walls. The problem is solved by successive iterations in which a system of equations is constructed and solved for each cross-section. In this method, the differential equations in the spanwise directions are formulated and solved using a finite-differences scheme which allows simple adaptation of the spanwise discretization mesh during iterations.

Thermoelastic analysis of space structures in periodic motion

Large truss-type space structures undergoing periodic motion are analyzed using Fourier decomposition in time and finite elements in space. Both the temperature field and the displacement field in the structure are found. Any symmetry which the structure may possess with respect to the axis of rotation is exploited in the numerical scheme and leads to saving in computational cost. A general algorithm is devised to calculate the external heat flux distribution. Numerical examples, which include a rotating cylindrically shaped structure and a parabolic antenna dish in orbit around Earth, are presented. The transition between the quasisteady state and the dynamic state in both the thermal and the elastic analyses is discussed in view of the numerical results.

Adaptive Estimation Methodology for Helicopter Blade Structural Damage Detection

A new, multiple model approach for detection and identie cation of structural damage in a rotating helicopter blade is presented. A full-scale rotor analysis using a detailed model of the hingeless blade elastic behavior and dynamics is carried out. Several stiffness damage levels and locations are considered, and a set of Kalman e lters is constructed accordingly. The best e tting model is determined in a probabilistic manner. Because the new method is model-based, the need for a training stage is eliminated, and a wide range of e ight regimes can be handled. Moreover, process and measurement noises are treated inherently, contributing to the superiority of the method over previously published related methods. A Monte Carlo simulation study is used to provide a comprehensive analysis of the statistical nature of the method. Single-blade analysis results demonstrate excellent identie cation capability and good damage detection in the presence of a relatively high level of noise. The case of damage located near the blade’ s root combined with a sensor near the tip produces a high damage identie cation probability. In less detectable cases, such as damage located in midspan, a simple statistical procedure enables achieving a high detection probability along with a low false alarm rate.

A refined nonlinear analysis of pre-twisted composite blades

A nonlinear formulation for the structural behavior of initially twisted solid and thin walled composite blades is presented. The model is designed to handle arbitrary thick solid cross-sections or general thin-walled geometries, and includes three-dimensional out-of-plane warping. The nonlinear scheme enables the inclusion of geometrical nonlinearities in the presence of large initial twist, and is based on a formulation that preserves three-dimensional effects and continuity of displacements, rotations and detailed warping distributions. A basic and important feature of the present analysis is the fact that the quasi-linear solutions that are employed throughout the iterative process are executed for the blade as a whole. This allows one to determine and preserve complex three-dimensional effects including warping continuity which are usually lost by standard segment discretization schemes. A study of the combined effect of initial twist and composite induced elastic couplings is presented in addition to a correlation with nonlinear experimental data.