A higher order model for thin-walled structures with deformable cross-sections

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.

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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

Applied Sciences ◽

10.3390/app9235186 ◽

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.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1019.96 ◽

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.

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Crashing Behaviour Analysis of TWB Tubular Structures with Different Cross-Sections

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.814.159 ◽

2013 ◽

Vol 814 ◽

pp. 159-164

Author(s):

Vlad Andrei Ciubotariu

Keyword(s):

Finite Element ◽

Cross Sections ◽

Fuel Efficiency ◽

Tubular Structures ◽

Tailor Welded Blanks ◽

Thin Walled Structures ◽

Prediction And Control ◽

Thin Walled ◽

Crushing Behavior ◽

Bimetallic Structures

The present paper investigates the crashing behavior and energy absorption characteristics of thin-walled (tubular) structures with different cross-sections made from tailor welded blanks (TWB) which were subject of axial quasistatic loadings. Resulted data were obtained by using explicit nonlinear finite element code LS_Dyna V971. Implementing the TWB into the auto industry was an efficient method to decrease the general weight of different structures. By far, these kind of bimetallic structures are largely utilized in auto and naval industries because it led to important decrease of scarp quantities and general manufacturing costs, improved material use and probably the most important, great fuel efficiency. After reviewing the literature it was concluded that proper combination between mechanical characteristics of sheet metals, different thicknesses and cross-section shapes into the same thin-walled structure is far too little researched and understood. The aims of this study are better understandings of the crashing behavior regarding thin-walled structure with various cross-sections made from TWB blanks subject to quasistatic loadings. The non-linear finite element platform LS_Dyna V971 was used for the numerical analysis of the crushing behavior regarding the thin-walled structures. Having two materials constituting the thin-walled structures, the crashing behavior changed during the quasistatic loading. Thus, the crashing inertia of the structure is somehow limited and controlled. It is noted that material ratio should not be randomly chosen due to the unexpected crashing mode which could aggravate the prediction and control of the crashing behavior of the thin-walled structure.

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