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.

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.

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.

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 Three-dimensional beam element for pre- and post-buckling analysis of thin-walled beams in multibody systems

2021 ◽  
Author(s):  
J. B. Jonker
Keyword(s):  
Stability Analysis ◽  
Cross Section ◽  
Multibody Systems ◽  
Three Dimensional ◽  
Beam Element ◽  
Second Order ◽  
Open Section ◽  
Post Buckling ◽  
Thin Walled ◽  
Deformation Modes

AbstractThis paper presents a three-dimensional beam element for stability analysis of elastic thin-walled open-section beams in multibody systems. The beam model is based on the generalized strain beam formulation. In this formulation, a set of independent deformation modes is defined which are related to dual stress resultants in a co-rotational frame. The deformation modes are characterized by generalized strains or deformations, expressed as analytical functions of the nodal coordinates referred to the global coordinate system. A nonlinear theory of non-uniform torsion of open-section beams is adopted for the derivation of the elastic and geometric stiffness matrices. Both torsional-related warping and Wagner’s stiffening torques are taken into account. Second order approximations for the axial elongation and bending curvatures are included by additional second order terms in the expressions for the deformations. The model allows to study the buckling and post-buckling behaviour of asymmetric thin-walled beams with open cross-section that can undergo moderately large twist rotations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. Some validation examples illustrate the accuracy and computational efficiency of the new beam element in the analysis of the buckling and post-buckling behaviour of thin-walled beams under various loads and (quasi)static boundary conditions. Finally, applications to multibody problems are presented, including the stability analysis of an elementary two-flexure cross-hinge mechanism.

A Formulation for the Shear Coefficient of Thin-Walled Prismatic Beams

1985 ◽  
Vol 29 (01) ◽  
pp. 51-58 ◽  
Author(s):  
Shankaranarayana U. Bhat ◽  
Joao G. de Oliveira
Keyword(s):  
Single Cell ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Present Approach ◽  
Compatibility Conditions ◽  
Shear Coefficient ◽  
Thin Walled ◽  
Definition Of ◽  
Integrated Or

A formulation for the shear coefficient of arbitrary monosymmetric thin-walled cross sections is proposed. The derivation uses integrated or average displacements and rotation, and the effect of Poisson's ratio is taken into account. In contrast to earlier formulations in which three-dimensional stress and displacement distributions for solid sections should first be assumed, the present approach applies directly to thin-walled cross sections. The theory is also valid in the case where the cross section contains several closed cells, and this requires the definition of compatibility conditions which take Poisson's effect into account. Some simple examples are given, which show that the shear coefficient increases by a few percent when Poisson's effect is considered, in a manner similar to what happens with open or single cell sections.

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.

ANALYSIS OF THIN-WALLED BEAMS VIA A ONE-DIMENSIONAL UNIFIED FORMULATION THROUGH A NAVIER-TYPE SOLUTION

2011 ◽  
Vol 03 (03) ◽  
pp. 407-434 ◽  
Author(s):  
G. GIUNTA ◽  
F. BISCANI ◽  
S. BELOUETTAR ◽  
E. CARRERA
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Approximation Order ◽  
Geometrical Parameters ◽  
Type Solution ◽  
Dimensional Finite Element ◽  
Thin Walled ◽  
Three Dimensional Finite Element ◽  
Beam Theories

A unifying approach to formulate several axiomatic theories for beam structures is addressed in this paper. A N-order polynomials approximation is assumed on the beam cross-section for the displacement unknown variables, N being a free parameter of the formulation. Classical beam theories, such as Euler–Bernoulli's and Timoshenko's, are obtained as particular cases. According to the proposed unified formulation, the governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. The linear static analysis of thin-walled beams is carried out through a closed form, Navier-type solution. Simply supported beams are, therefore, presented. Box, C- and I-shaped cross-sections are accounted for. Slender and deep beams are investigated. Bending and torsional loadings are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigation has shown that the proposed unified formulation yields the complete three-dimensional displacement and stress fields for each cross-section as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam and the loading conditions.

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