Parametric Studies on Bending of Twisted Timoshenko Beams Under Complex Loadings

2012 ◽  
Vol 28 (1) ◽  
pp. N1-N6 ◽  
Author(s):  
W.-R. Chen
Keyword(s):  
Twist Angle ◽  
Width Ratio ◽  
Algebraic Equations ◽  
Equilibrium Equations ◽  
Static Loads ◽  
Parametric Studies ◽  
Element Approach ◽  
Minimum Potential ◽  
Parametric Analyses ◽  
Twisted Beam

ABSTRACTStatic bending of a twisted Timoshenko beam subjected to combined transverse and axial loadings is studied. The equilibrium equations are established in the twist coordinates by applying the principle of minimum potential energy. The governing equations are then reduced into solvable algebraic equations using a finite element approach. The effects of the twist angle, thickness-to-width ratio, length-to-thickness ratio, loading and boundary conditions on the static bending characteristics of the twisted beams are investigated. The present parametric analyses will provide engineers a good insight into the influence of various structural aspects of the twisted beam on its response to different static loads.

Transverse Vibrations of a Rotating Twisted Timoshenko Beam Under Axial Loading

1993 ◽  
Vol 115 (3) ◽  
pp. 285-294 ◽  
Author(s):  
W.-R. Chen ◽  
L. M. Keer
Keyword(s):  
Timoshenko Beam ◽  
Twist Angle ◽  
Equations Of Motion ◽  
Axial Loading ◽  
Beam Theory ◽  
The Finite Element Method ◽  
Bending Vibrations ◽  
Parametric Studies ◽  
General Eigenvalue Problem ◽  
Twisted Beam

Transverse bending vibrations of a rotating twisted beam subjected to an axial load and spinning about its axial axis are established by using the Timoshenko beam theory and applying Hamilton’s Principle. The equations of motion of the twisted beam are derived in the twist nonorthogonal coordinate system. The finite element method is employed to discretize the equations of motion into time-dependent ordinary differential equations that have gyroscopic terms. A symmetric general eigenvalue problem is formulated and used to study the influence of the twist angle, rotational speed, and axial force on the natural frequencies of Timoshenko beams. The present model is useful for the parametric studies to understand better the various dynamic aspects of the beam structure affecting its vibration behavior.

scholarly journals An axisymmetric problem for a penny-shaped crack under the influence of the Steigmann–Ogden surface energy

2021 ◽  
Vol 477 (2248) ◽  
Author(s):  
Anna Y. Zemlyanova
Keyword(s):  
Surface Energy ◽  
Numerical Procedure ◽  
Material System ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Penny Shaped Crack ◽  
Normal Traction ◽  
Parametric Studies ◽  
Shaped Crack ◽  
Isotropic Elastic Medium

A problem for a nanosized penny-shaped fracture in an infinite homogeneous isotropic elastic medium is considered. The fracture is opened by applying an axisymmetric normal traction to its surface. The surface energy in the Steigmann–Ogden form is acting on the boundary of the fracture. The problem is solved by using the Boussinesq potentials represented by the Hankel transforms of certain unknown functions. With the help of these functions, the problem can be reduced to a system of two singular integro-differential equations. The numerical solution to this system can be obtained by expanding the unknown functions into the Fourier–Bessel series. Then the approximations of the unknown functions can be obtained by solving a system of linear algebraic equations. Accuracy of the numerical procedure is studied. Various numerical examples for different values of the surface energy parameters are considered. Parametric studies of the dependence of the solutions on the mechanical and the geometric parameters of the system are undertaken. It is shown that the surface parameters have a significant influence on the behaviour of the material system. In particular, the presence of surface energy leads to the size-dependency of the solutions and smoother behaviour of the solutions near the tip of the crack.

The Stress Response of Radially Polarized Rotating Piezoelectric Cylinders

2003 ◽  
Vol 70 (3) ◽  
pp. 426-435 ◽  
Author(s):  
D. Galic ◽  
C. O. Horgan
Keyword(s):  
Analytic Solution ◽  
Coupled System ◽  
Special Problem ◽  
Algebraic Equations ◽  
Equilibrium Equations ◽  
Closed Form Solutions ◽  
Linear Algebraic Equations ◽  
Constant Potential ◽  
Radially Polarized ◽  
Fundamental Boundary

Recent advances in smart structures technology have lead to a resurgence of interest in piezoelectricity, and in particular, in the solution of fundamental boundary value problems. In this paper, we develop an analytic solution to the axisymmetric problem of an infinitely long, radially polarized, radially orthotropic piezoelectric hollow circular cylinder rotating about its axis at constant angular velocity. The cylinder is subjected to uniform internal pressure, or a constant potential difference between its inner and outer surfaces, or both. An analytic solution to the governing equilibrium equations (a coupled system of second-order ordinary differential equations) is obtained. On application of the boundary conditions, the problem is reduced to solving a system of linear algebraic equations. The stress distribution in the tube is obtained numerically for a specific piezoceramic of technological interest, namely PZT-4. For the special problem of a uniformly rotating solid cylinder with traction-free surface and zero applied electric charge, explicit closed-form solutions are obtained. It is shown that for certain piezoelectric solids, stress singularities at the origin can occur analogous to those occurring in the purely mechanical problem for radially orthotropic elastic materials.

scholarly journals Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity

2019 ◽  
Vol 24 (1) ◽  
pp. 17
Author(s):  
Clément Olivier ◽  
David Ryckelynck ◽  
Julien Cortial
Keyword(s):  
Constitutive Equations ◽  
Surrogate Model ◽  
Reference Model ◽  
Data Representation ◽  
Differential Algebraic Equations ◽  
Constitutive Law ◽  
Algebraic Equations ◽  
Tensor Representation ◽  
Novel Approach ◽  
Parametric Studies

This work presents a novel approach to construct surrogate models of parametric differential algebraic equations based on a tensor representation of the solutions. The procedure consists of building simultaneously an approximation given in tensor-train format, for every output of the reference model. A parsimonious exploration of the parameter space coupled with a compact data representation allows alleviating the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients.

ANALYSIS OF HYDRAULIC STRUCTURES SUPPOSING THEIR SIMULATION IN THE FORM OF PRISMATIC SYSTEMS

2016 ◽  
Vol 6 (4) ◽  
pp. 59-63
Author(s):  
Elena S. VRONSKAYA
Keyword(s):  
Complex Structure ◽  
Hydroelectric Station ◽  
Computing System ◽  
Hydraulic Structures ◽  
Algebraic Equations ◽  
Equilibrium Equations ◽  
Strain Compatibility ◽  
Nodal Lines ◽  
Edge Conditions ◽  
Series Transformation

A new method for analysis of hydraulic structures supposing their simulation in the form of prismatic systems is proposed. Algorithm and computing system effectiveness is provided by smaller - in comparison with digital methods - equations resolution order and high accuracy of results. The main part of paper is devoted to development of algorithm of automated formation of geometric structure, edge conditions as well as of equilibrium equations and equations of strain compatibility in nodal lines of complex structure with free cinfiguration. Algorithm of equations formulation is based on solution of differential equations of plate equilibrium through Fourier series transformation and start conditions use resulting in formation of resolving system of algebraic equations where initial parameters and final values of forces are defined. The example of structural analysis of Volzhskaya hydroelectric station building during different work modes is given.

scholarly journals A Novel Technique for Predicting the Thermal Behavior of Stratospheric Balloon

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Yunpeng Ma ◽  
Jun Huang ◽  
Mingxu Yi
Keyword(s):  
Thermal Behavior ◽  
Operational Matrix ◽  
Algebraic Equations ◽  
Gas Temperature ◽  
Equilibrium Equations ◽  
Legendre Wavelets ◽  
Novel Technique ◽  
Stratospheric Balloon ◽  
Novel Method ◽  
Operational Matrix Of Integration

This paper is devoted to introduce a novel method of the operational matrix of integration for Legendre wavelets in order to predict the thermal behavior of stratospheric balloons on float at high altitude in the stratosphere. Radiative and convective heat transfer models are also developed to calculate absorption and emission heat of the balloon film and lifting gas within the balloon. Thermal equilibrium equations (TEE) for the balloon system at daytime and nighttime are shown to predict the thermal behavior of stratospheric balloons. The properties of Legendre wavelets are used to reduce the TEE to a nonlinear system of algebraic equations which is solved by using a suitable numerical method. The approximations of the thermal behavior of the balloon film and lifting gas within the balloon are derived. The diurnal variations of the film and lifting gas temperature at float conditions are investigated, and the efficiency of the proposed method is also confirmed.

scholarly journals Equivalent stabilizing force of members parabolically compressed by longitudinally variable axial force

2019 ◽  
Vol 262 ◽  
pp. 09004
Author(s):  
Antoni Biegus ◽  
Dariusz Czepiżak
Keyword(s):  
Force Constant ◽  
Axial Force ◽  
Central Zone ◽  
Force Distribution ◽  
Support Zone ◽  
Axial Forces ◽  
Parametric Studies ◽  
Parametric Analyses

The EN 1993-1-1 model of equivalent stabilizing force qd and Rd of bracings conservatively assumes that the braced member is compressed with a force constant along its length. This assumption is incorrect since the axial force distribution varies along the length of the braced member. As a result, the braced member generates equivalent stabilizing forces different from equivalent force qd and Rd acc. to EN 1993-1-1. This paper presents parametric studies of the equivalent stabilizing forces of the braced, compression top chord of roof trusses. The girder’s top chord is compressed parabolically by a variable axial force. The values of the axial compressive forces is: Nsupp in the support zone of truss and Nspan in the central zone of truss. Parametric analyses of the equivalent stabilizing force and the stress of the purlins and the bracings depending on axial forces Nsupp and Nspan in the braced member were carried out. The investigated problem is illustrated with exemplary calculations of the equivalent force in trusses.

scholarly journals Elastic Stability Analysis of a Two-Layered Functionally Graded Cylindrical Shell under Axial Compression with the use of Energy Approach

2009 ◽  
Vol 18 (6) ◽  
pp. 096369350901800 ◽  
Author(s):  
H. Sepiani ◽  
A. Rastgoo ◽  
M. Ahmadi ◽  
A.Ghorbanpour Arani ◽  
K. Sepanloo
Keyword(s):  
Cylindrical Shell ◽  
Potential Energy ◽  
Axial Compression ◽  
Elastic Layer ◽  
Elastic Stability ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Minimum Potential Energy ◽  
Equilibrium Equations ◽  
Minimum Potential

This paper investigates the elastic axisymmetric buckling of a thin, simply supported functionally graded (FG) cylindrical shell embedded with an elastic layer under axial compression. The analysis is based on energy method and simplified nonlinear strain-displacement relations for axial compression. Material properties of functionally graded cylindrical shell are considered graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Using minimum potential energy together with Euler equations, equilibrium equations are obtained. Consequently, stability equation of functionally graded cylindrical shell with an elastic layer is acquired by means of minimum potential energy theory and Trefftz criteria. Another analysis is made using the equivalent properties of FG material. Numerical results for stainless steel-ceramic cylindrical shell and aluminum layer are obtained and critical load curves are analyzed for a cylindrical shell with an elastic layer. A comparison is made to the results in the literature. The results show that the elastic stability of functionally graded cylindrical shell with an elastic layer is dependent on the material composition and FGM index factor, and the shell geometry parameters and it is concluded that the application of an elastic layer increases elastic stability and significantly reduces the weight of cylindrical shells.

A Coupled Two Degree of Freedom Model for Nano/Micromirrors Under van der Waals Force

2012 ◽  
Author(s):  
Hamid Moeenfard ◽  
Ali Darvishian ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Coupled Model ◽  
Bending Stiffness ◽  
Degree Of Freedom ◽  
Instability Mode ◽  
Equilibrium Equations ◽  
Bending Mode ◽  
Minimum Potential ◽  
Vdw Force ◽  
Torsion Stiffness ◽  
Two Degree Of Freedom

The current paper presents a two degree of freedom model for the problem of nano/micromirrors under the effect of vdW force. Energy method, the principal of minimum potential energy is employed for finding the equilibrium equations governing the deflection and the rotation of the nano/micromirror. Then using the implicit function theorem, a coupled bending-torsion model is presented for the pull-in characteristics of nano/micromirrors under vdW force and the concept of instability mode is introduced. It is observed that with increasing the ratio of the bending stiffness to the torsion stiffness, the dominant instability mode changes from bending mode to the torsion mode. It is shown that when the bending stiffness of the system is relatively low, the equilibrium point of a one degree of freedom torsion model considerably deviates from that of coupled model. The presented model in this paper can be used for safe and stable design of nano/micromirrors under vdW force.

Practical Modeling for Articulated Risers and Loading Columns

1984 ◽  
Vol 106 (4) ◽  
pp. 444-450 ◽  
Author(s):  
J. F. McNamara ◽  
M. Lane
Keyword(s):  
Ship Motions ◽  
Random Waves ◽  
Efficient Design ◽  
Time Step ◽  
Design Studies ◽  
Large Rotations ◽  
Parametric Studies ◽  
Element Approach ◽  
Large Time Step ◽  
Nonlinear Static

An efficient method for the analysis of the linear and nonlinear static and dynamic motions of offshore systems such as risers and single-leg mooring towers is presented. The technique is based on the finite element approach using connected coordinates for arbitrary large rotations and includes terms due to loads such as buoyancy, gravity, random waves, currents, ship motions and Morison’s equation. Practical features include the addition of intermediate articulations and modeling of the loading arm between the riser and associated tanker. Parametric studies are presented to show that stable and accurate results are obtained using relatively large time step increments leading to efficient design studies.

Sign in / Sign up

Export Citation Format

Share Document