scholarly journals A Simplified Approach to Identify Sectional Deformation Modes of Thin-Walled Beams with Prismatic Cross-Sections

2018 ◽  
Vol 8 (10) ◽  
pp. 1847 ◽  
Author(s):  
Lei Zhang ◽  
Weidong Zhu ◽  
Aimin Ji ◽  
Liping Peng
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Higher Order ◽  
Basis Functions ◽  
Beam Model ◽  
Linear Superposition ◽  
Simplified Approach ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Deformation Modes

In this paper, a simplified approach to identify sectional deformation modes of prismatic cross-sections is presented and utilized in the establishment of a higher-order beam model for the dynamic analyses of thin-walled structures. The model considers the displacement field through a linear superposition of a set of basis functions whose amplitudes vary along the beam axis. These basis functions, which describe basis deformation modes, are approximated from nodal displacements on the discretized cross-section midline, with interpolation polynomials. Their amplitudes acting in the object vibration shapes are extracted through a modal analysis. A procedure similar to combining like terms is then implemented to superpose basis deformation modes, with equal or opposite amplitude, to produce primary deformation modes. The final set of the sectional deformation modes are assembled with primary deformation modes, excluding the ones constituting conventional modes. The derived sectional deformation modes, hierarchically organized and physically meaningful, are used to update the basis functions in the higher-order beam model. Numerical examples have also been presented and the comparison with ANSYS shell model showed its accuracy, efficiency, and applicability in reproducing three-dimensional behaviors of thin-walled structures.

scholarly journals On the Identification of Sectional Deformation Modes of Thin-Walled Structures with Doubly Symmetric Cross-Sections Based on the Shell-Like Deformation

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 759 ◽  
Author(s):  
Lei Zhang ◽  
Aimin Ji ◽  
Weidong Zhu ◽  
Liping Peng
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Plate Theory ◽  
Interpolation Method ◽  
Three Dimensional ◽  
Residual Deformation ◽  
Linear Superposition ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Deformation Modes

In this paper, a new approach is proposed to identify sectional deformation modes of the doubly symmetric thin-walled cross-section, which are to be employed in formulating a one-dimensional model of thin-walled structures. The approach considers the three-dimensional displacement field of the structure as the linear superposition of a set of sectional deformation modes. To retrieve these modes, the modal analysis of a thin-walled structure is carried out based on shell/plate theory, with the shell-like deformation shapes extracted. The components of classical modes are removed from these shapes based on a novel criterion, with residual deformation shapes left. By introducing benchmark points, these shapes are further classified into several deformation patterns, and within each pattern, higher-order deformation modes are derived by removing the components of identified ones. Considering the doubly symmetric cross-section, these modes are approximated with shape functions applying the interpolation method. The identified modes are finally used to deduce the governing equations of the thin-walled structure, applying Hamilton’s principle. Numerical examples are also presented to validate the accuracy and efficiency of the new model in reproducing three-dimensional behaviors of thin-walled structures.

A super-convergent thin-walled 3D beam element for analysis of laminated composite structures with arbitrary cross-section

2021 ◽  
pp. 1-23
Author(s):  
M. Talele ◽  
M. van Tooren ◽  
A. Elham
Keyword(s):  
Cross Sections ◽  
Composite Structures ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Beam Element ◽  
Arbitrary Cross Section ◽  
Beam Model ◽  
Cross Sectional ◽  
Thin Walled ◽  
The Cross

Abstract An efficient, fully coupled beam model is developed to analyse laminated composite thin-walled structures with arbitrary cross-sections. The Euler–Lagrangian equations are derived from the kinematic relationships for a One-Dimensional (1D) beam representing Three-Dimensional (3D) deformations that take into account the cross-sectional stiffness of the composite structure. The formulation of the cross-sectional stiffness includes all the deformation effects and related elastic couplings. To circumvent the problem of shear locking, exact solutions to the approximating Partial Differential Equations (PDEs) are obtained symbolically instead of by numerical integration. The developed locking-free composite beam element results in an exact stiffness matrix and has super-convergent characteristics. The beam model is tested for different types of layup, and the results are validated by comparison with experimental results from literature.

Buckling of thin-walled structures through a higher order beam model

2017 ◽  
Vol 180 ◽  
pp. 104-116 ◽  
Author(s):  
R.F. Vieira ◽  
F.B.E. Virtuoso ◽  
E.B.R. Pereira
Keyword(s):  
Higher Order ◽  
Beam Model ◽  
Thin Walled Structures ◽  
Thin Walled

scholarly journals A Novel Approach to Perform the Identification of Cross-Section Deformation Modes for Thin-Walled Structures in the Framework of a Higher Order Beam Theory

2019 ◽  
Vol 9 (23) ◽  
pp. 5186
Author(s):  
Lei Zhang ◽  
Aimin Ji ◽  
Weidong Zhu
Keyword(s):  
Cross Section ◽  
Higher Order ◽  
Preliminary Deformation ◽  
Structural Behaviour ◽  
Order Model ◽  
Thin Walled Structures ◽  
Novel Approach ◽  
Generalized Eigenvectors ◽  
Thin Walled ◽  
Deformation Modes

This paper presents a novel approach to identify cross-section deformation modes for thin-walled structures by assembling preliminary deformation modes (PDM) considering their participation in free vibration modes. These PDM, defined over the cross-section through kinematic concepts, are integrated in the governing equations of a higher order model and then uncoupled in the form of generalized eigenvectors. The eigenvectors are deemed to inherit the attributes of structural behaviours and can serve as the basis to assemble PDM. Accordingly, a criterion was developed to handle the eigenvectors, pursuing (i) the clustering of PDM that participate in a same structural behaviour, (ii) the assignation of the corresponding weights that indicate their participation and (iii) the decomposition of an amplitude function when it is related to several structural behaviours. Moreover, a numbering system was proposed to hierarchically organize the deformation modes, which is conducive to a reduced higher order model. The main features of this approach are found in its ability to be performed in a more operational way and its nature to give deformation modes physical interpretation inherited from the dynamic behaviours. The versatility of the approach was validated through both numerical examples and comparisons with other theories.

scholarly journals A new approach to the identification of distortion modes of thin-walled structures based on plate/shell theory

2019 ◽  
Vol 278 ◽  
pp. 03005
Author(s):  
Lei Zhang ◽  
Weidong Zhu ◽  
Aimin Ji ◽  
Liping Peng
Keyword(s):  
Cross Section ◽  
Shell Theory ◽  
Mode Shapes ◽  
Beam Model ◽  
Linear Superposition ◽  
New Approach ◽  
Thin Walled Structures ◽  
Dynamic Analyses ◽  
Thin Walled ◽  
The Cross

In this paper, a new approach to identify cross-section deformation modes is presented and utilized in the establishment of a high-order beam model for dynamic analyses of thin-walled structures. Towards this end, a systematic procedure to extract cross-section in-plane vibration shapes for a thin-walled cross-section is developed based on elastic plate/shell theory. Then the distortion shapes are separated from vibration shapes by removing the components of classic modes involved with the minimum value problem of 2-norm. Sequentially, curve fitting method is utilized to approximate the distortion shape functions along the cross-section midline. It should be noticed that these distortion modes are arranged in hierarchy consistent with the order that they are identified and the number of distortions to be identified depends on the required model precision. Based on this, Hamilton's principle is applied to formulate the dynamic governing equations of the beam by constructing its displacement field with the linear superposition of the cross-section mode shapes including distortions. Numerical examples are also presented to validate the new approach and to demonstrate its efficiency in the reproduction of three-dimensional behaviours of thin-walled structures in dynamic analyses.

Numerical Investigation of Cross-Section on Aluminum A6063 Thin-Walled Structures under Low-Velocity Impact Loading

2014 ◽  
Vol 1019 ◽  
pp. 96-102
Author(s):  
Ali Taherkhani ◽  
Ali Alavi Nia
Keyword(s):  
Energy Absorption ◽  
Cross Section ◽  
Cross Sections ◽  
Peak Load ◽  
Circular Cross Section ◽  
Absorption Capacity ◽  
Energy Absorption Capacity ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Crush Strength

In this study, the energy absorption capacity and crush strength of cylindrical thin-walled structures is investigated using nonlinear Finite Elements code LS-DYNA. For the thin-walled structure, Aluminum A6063 is used and its behaviour is modeled using power-law equation. In order to better investigate the performance of tubes, the simulation was also carried out on structures with other types of cross-sections such as triangle, square, rectangle, and hexagonal, and their results, namely, energy absorption, crush strength, peak load, and the displacement at the end of tubes was compared to each other. It was seen that the circular cross-section has the highest energy absorption capacity and crush strength, while they are the lowest for the triangular cross-section. It was concluded that increasing the number of sides increases the energy absorption capacity and the crush strength. On the other hand, by comparing the results between the square and rectangular cross-sections, it can be found out that eliminating the symmetry of the cross-section decreases the energy absorption capacity and the crush strength. The crush behaviour of the structure was also studied by changing the mass and the velocity of the striker, simultaneously while its total kinetic energy is kept constant. It was seen that the energy absorption of the structure is more sensitive to the striker velocity than its mass.

Sign in / Sign up

Export Citation Format

Share Document