skip to main content


This content will become publicly available on September 12, 2024

Title: A Fourier‐series numerical approach for the analysis of tubular members
Abstract

This paper provides an efficient and robust numerical solution for the linear buckling analysis of tubular members, such as the supporting tower structures of wind turbines. The method uses Fourier‐series approximations for the displacement functions. Longitudinal discretization can optionally be applied, i.e., the member can be divided into segments. The strain‐displacement relationship directly considers the curved geometry. The implementation allows for arbitrary support conditions. Four pure loading situations are considered, uniform – in each segment – along the length: normal force, bending moment, torque, and shear force; however, they can arbitrarily be combined, as is commonly occurring in wind turbine towers. The applied methodology results in a computational advantage compared to the shell finite element method, while still maintaining much more generality and applicability compared with common analytical solutions. Furthermore, the method is supplemented with features, as spectral analysis and buckling length calculation.

 
more » « less
NSF-PAR ID:
10479736
Author(s) / Creator(s):
 ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
ce/papers
Volume:
6
Issue:
3-4
ISSN:
2509-7075
Format(s):
Medium: X Size: p. 1139-1144
Size(s):
p. 1139-1144
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    We previously introduced the use of DNA molecules for calibration of biophysical force and displacement measurements with optical tweezers. Force and length scale factors can be determined from measurements of DNA stretching. Trap compliance can be determined by fitting the data to a nonlinear DNA elasticity model, however, noise/drift/offsets in the measurement can affect the reliability of this determination. Here we demonstrate a more robust method that uses a linear approximation for DNA elasticity applied to high force range (25–45 pN) data. We show that this method can be used to assess how small variations in microsphere sizes affect DNA length measurements and demonstrate methods for correcting for these errors. We further show that these measurements can be used to check assumed linearities of system responses. Finally, we demonstrate methods combining microsphere imaging and DNA stretching to check the compliance and positioning of individual traps. 
    more » « less
  2. Summary

    A new topology optimization scheme called the projection‐based ground structure method (P‐GSM) is proposed for linear and nonlinear topology optimization designs. For linear design, compared to traditional GSM which are limited to designing slender members, the P‐GSM can effectively resolve this limitation and generate functionally graded lattice structures. For additive manufacturing‐oriented design, the manufacturing abilities are the key factors to constrain the feasible design space, for example, minimum length and geometry complexity. Conventional density‐based method, where each element works as a variable, always results in complex geometry with large number of small intricate features, while these small features are often not manufacturable even by 3D printing and lose its geometric accuracy after postprocessing. The proposed P‐GSM is an effective method for controlling geometric complexity and minimum length for optimal design, while it is capable of designing self‐supporting structures naturally. In optimization progress, some bars may be disconnected from each other (floating in the air). For buckling‐induced design, this issue becomes critical due to severe mesh distortion in the void space caused by disconnection between members, while P‐GSM has ability to overcome this issue. To demonstrate the effectiveness of proposed method, three different design problems ranging from compliance optimization to buckling‐induced mechanism design are presented and discussed in details.

     
    more » « less
  3. Abstract

    Geostationary weather satellites collect high‐resolution data comprising a series of images. The Derived Motion Winds (DMW) Algorithm is commonly used to process these data and estimate atmospheric winds by tracking features in the images. However, the wind estimates from the DMW Algorithm are often missing and do not come with uncertainty measures. Also, the DMW Algorithm estimates can only be half‐integers, since the algorithm requires the original and shifted data to be at the same locations, in order to calculate the displacement vector between them. This motivates us to statistically model wind motions as a spatial process drifting in time. Using a covariance function that depends on spatial and temporal lags and a drift parameter to capture the wind speed and wind direction, we estimate the parameters by local maximum likelihood. Our method allows us to compute standard errors of the local estimates, enabling spatial smoothing of the estimates using a Gaussian kernel weighted by the inverses of the estimated variances. We conduct extensive simulation studies to determine the situations where our method performs well. The proposed method is applied to the GOES‐15 brightness temperature data over Colorado and reduces prediction error of brightness temperature compared to the DMW Algorithm.

     
    more » « less
  4. Micro-electromagnetic actuators have been used in many fields and industries for systems such as microftuidic systems, positioning stages, and robotic manipulators. Small-scale electromagnetic actuators are able to provide rapid motion with high positioning accuracy. The actuator presented in this paper utilizes a displacement amplification mechanism to increase the maximum stroke length that can be achieved. The dynamics of this actuator are nonlinear due to the dependence of the applied force on gap distance between the coils and the amplification mechanism. This nonlinearity causes the performance of PID control to vary with respect to the displacement of the actuator. The control method proposed in this paper to limit the overshoot resulting from nonlinearity uses a combination of PID control and robust input shapers. Using robust input shapers to account for parameter variation across the workspace, the combined controller eliminates the overshoot while maintaining short settling times. Simulations are presented to demonstrate the performance of the proposed method. 
    more » « less
  5. Understanding thin sheets, ranging from the macro to the nanoscale, can allow control of mechanical properties such as deformability. Out-of-plane buckling due to in-plane compression can be a key feature in designing new materials. While thin-plate theory can predict critical buckling thresholds for thin frames and nanoribbons at very low temperatures, a unifying framework to describe the e↵ects of thermal fluctuations on buckling at more elevated temperatures presents subtle difficulties. We develop and test a theoretical approach that includes both an in-plane compression and an outof- plane perturbing field to describe the mechanics of thermalised ribbons above and below the buckling transition. We show that, once the elastic constants are renormalised to take into account the ribbon’s width (in units of the thermal length scale), we can map the physics onto a mean-field treatment of buckling, provided the length is short compared to a ribbon persistence length. Our theoretical predictions are checked by extensive molecular dynamics simulations of thin thermalised ribbons under axial compression. 
    more » « less