A one-dimensional model for computing forced nonlinear vibration of thin-walled composite beams with open variable cross-sections

2020 ◽  
pp. 107211
Author(s):  
Ahmed Elkaimbillah ◽  
Bouazza Braikat ◽  
Foudil Mohri ◽  
Noureddine Damil
Keyword(s):  
Nonlinear Vibration ◽  
Cross Sections ◽  
Composite Beams ◽  
Variable Cross ◽  
Dimensional Model ◽  
One Dimensional ◽  
Thin Walled ◽  
Forced Nonlinear Vibration

Modal Analysis of Thin Walled Multi-Cell Multi-Tapered Composite Beams of Closed Cross Sections

2014 ◽  
Vol 629 ◽  
pp. 82-88 ◽  
Author(s):  
Sohail Ahmed ◽  
M.N. Ahmed
Keyword(s):  
Modal Analysis ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Aerospace Industry ◽  
Composite Beams ◽  
Wind Gust ◽  
Aircraft Wing ◽  
Model Accuracy ◽  
Finite Element Package ◽  
Thin Walled

This paper explicitly highlights the modal analysis of thin walled multi-cell multi-tapered composite beams in cantilever configurations, using MSC Patran / Nastran finite element package. Initially, the verification of the model was done with the analytical results in order to ensure the model accuracy. All the multi-tapered beams under examination are composed of closed section and three cell configuration. There is a vivid description of all the effects of composite material and stacking sequence on the modal frequencies. It also suggests the ways to shift the natural frequencies of the multi-tapered beams. This paper verifies the effects of different geometrical configurations of beams (tapered angles, lengths and point of variation of tapered angles) on the modal frequencies. This research is also useful in aerospace industry while designing the aircraft wing, which would experience the vibrations due to wind gust and engine cycles.

scholarly journals Energy Absorption of Aluminium Extrusions Filled with Cellular Materials Under Axial Crushing: Study of the Interaction Effect

2020 ◽  
Vol 10 (23) ◽  
pp. 8510
Author(s):  
Javier Paz ◽  
Miguel Costas ◽  
Jordi Delgado ◽  
Luis Romera ◽  
Jacobo Díaz
Keyword(s):  
Energy Dissipation ◽  
Cross Sections ◽  
Interaction Effect ◽  
Unit Volume ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Polymeric Foam ◽  
Axial Crushing ◽  
Foam Filled ◽  
Thin Walled

This investigation focuses on the interaction effect during the quasi-static axial crushing of circular and square thin-walled aluminium extrusions filled with polymeric foam or cork. The increment in the absorbed energy due to interactions between materials was assessed using a validated numerical model calibrated with experimental material data. Simulations were run with variable cross-section dimensions, thickness, and foam density. The results were used to adjust the parameters of design formulas to predict the average crush forces of foam- and cork-filled thin-walled tubes. The analysis of the energy dissipation per unit volume revealed that the highest increments due to the interaction between materials appeared in the foam-filled square extrusions. Energy dissipation increased with higher density foams for both cross-sections due to a stronger constraint of the aluminium walls, and thus a reduction of the folding length. Thinner tube walls also delivered a higher improvement in the energy dissipation per unit volume than those with thicker walls. The contribution of friction was also quantified and investigated.

Analysis of Thin-Walled Closed Beams With General Quadrilateral Cross Sections

1999 ◽  
Vol 66 (4) ◽  
pp. 904-912 ◽  
Author(s):  
J. H. Kim ◽  
Y. Y. Kim
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Distortion Function ◽  
Element Formulation ◽  
Numerical Work ◽  
New Approach ◽  
One Dimensional ◽  
Static And Dynamic Analysis ◽  
Thin Walled ◽  
The One

This paper deals with the one-dimensional static and dynamic analysis of thin-walled closed beams with general quadrilateral cross sections. The coupled deformations of distortion as well as torsion and warping are investigated in this work. A new approach to determine the functions describing section deformations is proposed. In particular, the present distortion function satisfies all the necessary continuity conditions unlike Vlasov's distortion function. Based on these section deformation functions, a one-dimensional theory dealing with the coupled deformations is presented. The actual numerical work is carried out using two-node C0 finite element formulation. The present one-dimensional results for some static and free-vibration problems are compared with the existing and the plate finite element results.

scholarly journals APPLICATION OF SUPERELEMENTS IN STATIC ANALYSIS OF THIN‐WALLED STRUCTURES

2004 ◽  
Vol 10 (2) ◽  
pp. 113-122
Author(s):  
Ireneusz Kreja ◽  
Tomasz Mikulski ◽  
Czeslaw Szymczak
Keyword(s):  
Static Analysis ◽  
Standard Procedure ◽  
Dimensional Model ◽  
Fem Model ◽  
Shell Elements ◽  
One Dimensional ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Proper Solutions

A concept of a beam superelement is suggested as a new tool in the static analysis of structures made of thin‐walled members. This proposal seems to be especially attractive for treating the problems where the existing one‐dimensional models do not provide proper solutions. This class of problems includes, for instance, the torsion of thin‐walled beams with battens and the determination of the bimoment distribution at the nodes of frames made of thin‐walled members. The entire segment of the thin‐walled beam with warping stiffener or the whole node of the frame is modelled with shell elements. The stiffness matrix of such thin‐walled beam superelement can be estimated according to the standard procedure of the enforced unit displacements. The accuracy of the proposed one‐dimensional model has proved to be comparable to that offered by the detailed FEM model where the whole structure is represented by a very large number of shell elements.

AN ASYMPTOTIC ANALYSIS ON THE FORM OF NAGHDI TYPE ARCH MODEL

2008 ◽  
Vol 18 (03) ◽  
pp. 417-442 ◽  
Author(s):  
SHENG ZHANG
Keyword(s):  
Correction Factor ◽  
Cross Sections ◽  
Full Range ◽  
Relative Energy ◽  
Beam Model ◽  
Arch Model ◽  
Dimensional Model ◽  
One Dimensional ◽  
Shear Correction Factor ◽  
Transverse Shearing

We consider a one-dimensional model of generally curved elastic arches whose cross-sections are rectangular. The model is of Naghdi's type which is a generalization of the Timoshenko beam model, which allows bending, membrane and transverse shearing deformations. Its form is basically determined in the literature, except for the value of a shear correction factor. With this factor being set to 1, we prove that the modelling error in the interior relative energy norm is proportional to the arch thickness. This result holds for the full range of arch shapes and very general loads. Lower modelling accuracy is proven to hold up to the arch ends. Any shear correction factor other than 1 makes the model diverge from the elasticity theory when a significant shear is involved in the deformation.

scholarly journals Effect of local stiffeners and warping constraints on the buckling of symmetric open thin-walled beams with high warping stiffness

Meccanica ◽  
2021 ◽  
Author(s):  
G. Piana ◽  
E. Lofrano ◽  
A. Carpinteri ◽  
G. Ruta
Keyword(s):  
Cross Section ◽  
Bending Stiffness ◽  
Dimensional Model ◽  
One Dimensional ◽  
Practical Applications ◽  
Thin Walled ◽  
Compressive Buckling ◽  
The Way

AbstractLocal stiffeners affect the behaviour of thin-walled beams (TWBs). An in-house code based on a one-dimensional model proved effective in several instances of compressive buckling of TWBs but gave counterintuitive results for locally stiffened TWBs. To clarify the matter, we investigated TWBs with multi-symmetric double I cross-section, widely used in practical applications where high bending stiffness is required. Several samples were manufactured and stiffened on purpose, closing them over a small portion of the axis at different places. The samples were tested with end constraints accounting for various warping conditions. The experimental and numerical outputs from a commercial FEM code gave a key to overcome the unexpected results by the in-house code, paving the way for further studies.

Properties of the transition superoperator

1994 ◽  
Vol 72 (3-4) ◽  
pp. 152-161
Author(s):  
R. F. Snider ◽  
J. G. Muga
Keyword(s):  
Boltzmann Equation ◽  
Cross Sections ◽  
Separable Potential ◽  
Line Broadening ◽  
Dimensional Model ◽  
One Dimensional ◽  
Mathematical Arguments ◽  
The Subject ◽  
Spectral Line Broadening ◽  
Transition Operators

Two different transition superoperators naturally arise in physical theories. First, there is the abstract transition superoperator that arises in the quantum Boltzmann equation and collision cross sections. Second, there is a transition superoperator that arises in the theory of spectral line broadening. The latter is parameterized by the frequency of the light being observed. At present the standard method of evaluating the effects of transition superoperators is through the use of transition operators. However, the connection between transition superoperators and operators has been the subject of controversy while the diversity of transition superoperators and operators can be confusing. This paper reviews the basic definitions and methods of relating these quantities, exemplifying these properties by using a separable potential with explicit calculations for a particular one-dimensional model. In this way the validity of previously presented abstract mathematical arguments is demonstrated explicitly.

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