Numerical Modeling of Initial Stress Stiffening Effect on the Dynamic Behavior of Axisymmetric Shells

2021 ◽  
Vol 143 (5) ◽  
Author(s):  
Yacine Ben-Youssef ◽  
Youcef Kerboua ◽  
Aouni A. Lakis
Keyword(s):  
Finite Element ◽  
Initial Stress ◽  
Dynamic Behavior ◽  
Stiffness Matrix ◽  
Radial Pressure ◽  
Theoretical Research ◽  
Equilibrium Equations ◽  
Theoretical Formulation ◽  
Axisymmetric Shells ◽  
Stiffening Effect

Abstract This paper presents a numerical model to simulate the initial stress stiffening effect, induced by radial pressure and/or axial load on the dynamic behavior of axisymmetric shells. This effect is particularly important for thin shells since their bending stiffness is very small compared to membrane stiffness. The theoretical formulation is based on a combination of the finite element method and classical shell theory. For a perfect geometrical consistency, two semi-analytical finite elements, conical and cylindrical, are used to model axisymmetric shells. The displacement functions are derived from exact solutions of Sanders' shell equilibrium equations. The results obtained using this approach are remarkably accurate. The potential energy is calculated to estimate the initial stiffening effect using direct membrane forces per unit width and rotations about the orthogonal axes. The final stiffness matrix of each finite element is composed of the regular stiffness matrix and the added stiffness matrix generated by membrane loads. The frequencies of vibration are compared with those obtained in other experimental and theoretical research works and very good agreement is observed.

On the Unsymmetric Eigenproblem for the Buckling of Shells Under Pressure Loading

1983 ◽  
Vol 50 (1) ◽  
pp. 95-100 ◽  
Author(s):  
H. A. Mang ◽  
R. H. Gallagher
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hydrostatic Pressure ◽  
Stiffness Matrix ◽  
Circular Cylindrical Shell ◽  
The Finite Element Method ◽  
Equilibrium Equations ◽  
Buckling Loads ◽  
Large Rotations ◽  
Element Method

Consideration of the dependence of hydrostatic pressure on the displacements may result in significant changes of calculated buckling loads of thin arches and shells in comparison with loads calculated without consideration of this effect. The finite element method has made it possible to quantify these changes. On the basis of a shell theory of small displacements but moderately large rotations, this paper derives consistent incremental equilibrium equations for tracing, via the finite element method, the load-displacement path for thin shells subjected to nonuniform hydrostatic pressure and establishes the buckling condition from the incremental equilibrium equations. Within the framework of the finite element method, the character of hydrostatic pressure as one of a follower load is represented in the so-called pressure-stiffness matrix. For shells with loaded free edges, this matrix is unsymmetric. The principal objective of the present paper is to demonstrate that symmetrization of the pressure stiffness matrix resulting from linearization of the buckling condition yields buckling loads that are identical to the eigenvalues resulting from first-order perturbation analysis of the unsymmetric eigenproblem. A circular cylindrical shell with a free and a hinged end, subjected to hydrostatic pressure, is used as an example of the admissibility of symmetrizing the pressure stiffness matrix and for assessing its effect.

Approximate Explicit Calculation of First Vibration Frequencies of an Unsymmetrical High Speed Rotor

2003 ◽  
Author(s):  
J. F. Antoine ◽  
G. Abba ◽  
C. Sauvey
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Behavior ◽  
Stiffness Matrix ◽  
High Speed ◽  
Explicit Calculation ◽  
Beam Model ◽  
Element Analysis ◽  
Switched Reluctance ◽  
Reluctance Motor

In order to easily predict and optimize the dynamic behavior of a high speed switched reluctance motor, a full analytic model, that gives directly and quickly the three first eigenfrequencies of the rotor, is proposed. The rotor is modelled as a 3 DOF Timoshenko’s beam model. The stiffness matrix is calculated with the Castigliano’s second theorem in structural analysis, which allows to obtain explicitly the eigenfrequencies expression and prevents to use classical finite element analysis. The influence of design and material modifications is studied and the dynamic behavior quickly predicted. The calculation time needed for testing a geometry is strongly smaller than with a finite element analysis.

The Dynamic Stiffness Method for Linear Rotor-Bearing Systems

1996 ◽  
Vol 118 (3) ◽  
pp. 332-339 ◽  
Author(s):  
F. A. Raffa ◽  
F. Vatta
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Matrix Analysis ◽  
Theoretical Formulation ◽  
Dynamic Stiffness Matrix ◽  
Rotor Systems ◽  
Stiffness Method ◽  
Dynamic Stiffness Method ◽  
Rotor Bearing

The behavior of linear rotor-bearing systems is investigated by using the exact approach of the dynamic stiffness method, which entails the use of continuous rather than lumped models. In particular, the theoretical formulation for rotor systems with anisotropic bearings is developed by utilizing the complex representation of all the involved variables. The proposed formulation eventually leads to the 8 × 8 complex dynamic stiffness matrix of the rotating Timoshenko beam; this matrix proves to be related, by a simple rule, to the 4 × 4 dynamic stiffness matrix, which describes rotor systems with isotropic bearings. The method is first applied to the critical speeds evaluation of a simple rotor system with rigid supports; for this case, the exact results of the dynamic stiffness approach are compared to the usual convergence procedure of the finite element method. Successively, the steady-state unbalance response of two rotor systems with anisotropic supports is analyzed; for these examples, the dynamic stiffness results compare favorably with the results of the finite element and the transfer matrix analysis performed by other authors.

Load-induced stiffness matrix of plates

2002 ◽  
Vol 29 (1) ◽  
pp. 181-184 ◽  
Author(s):  
Shi-Jun Zhou
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Closed Form Solutions ◽  
Stiffness Matrices ◽  
Support Conditions ◽  
Stiffening Effect ◽  
Element Method

In this paper, a rectangular plate element for the finite-element method, which takes into consideration the stiffening effect of dead loads, is proposed. The element stiffness matrices that include the effect of dead loads are derived. The effect of dead loads on dynamic behaviors of plates is analyzed using the finite-element method. It is shown that the stiffness of plates increases when the effect of dead loads is included in the calculation and that the effect is more significant for plates with a smaller stiffness. The validity of the proposed procedure is confirmed by numerical examples. Although the finite-element results obtained are in agreement with the approximate closed-form solutions, the proposed method based on a finite-element formulation is more easily applied to practical structures under various support conditions and various types of dead loads.Key words: load-induced stiffness matrix of plate, stiffening effect of dead loads.

The Equilibrium Cell-Based Smooth Finite Element Method for Shakedown Analysis of Structures

2019 ◽  
Vol 16 (05) ◽  
pp. 1840013 ◽  
Author(s):  
P. L. H. Ho ◽  
C. V. Le ◽  
T. Q. Chu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimization Problem ◽  
Conic Programming ◽  
Equilibrium Equations ◽  
Shakedown Analysis ◽  
Numerical Examples ◽  
Elastic Stresses ◽  
Gauss Points ◽  
Element Method

This paper presents a novel equilibrium formulation, that uses the cell-based smoothed method and conic programming, for limit and shakedown analysis of structures. The virtual strains are computed using straining cell-based smoothing technique based on elements of discretized mesh. Fictitious elastic stresses are also determined within the framework of finite element method (CS-FEM)-based Galerkin procedure, and equilibrium equations for residual stresses are satisfied in an average sense at every cell-based smoothing cell. All constrains are imposed at only one point in the smoothing domains, instead of Gauss points as in a standard FEM-based procedure. The resulting optimization problem is then handled using the highly efficient solvers. Various numerical examples are investigated, and obtained solutions are compared with available results in the literature.

DYNAMIC BEHAVIOR OF TELESCOPIC CRANES BOOM

2013 ◽  
Vol 13 (01) ◽  
pp. 1350010 ◽  
Author(s):  
IOANNIS G. RAFTOYIANNIS ◽  
GEORGE T. MICHALTSOS
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Analytical Model ◽  
Constant Velocity ◽  
Steel Beam ◽  
Continuum Approach ◽  
Theoretical Formulation ◽  
Modal Superposition ◽  
Superposition Technique

Telescopic cranes are usually steel beam systems carrying a load at the tip while comprising at least one constant and one moving part. In this work, an analytical model suitable for the dynamic analysis of telescopic cranes boom is presented. The system considered herein is composed — without losing generality — of two beams. The first one is a jut-out beam on which a variable in time force is moving with constant velocity and the second one is a cantilever with length varying in time that is subjected to its self-weight and a force at the tip also changing with time. As a result, the eigenfrequencies and modal shapes of the second beam are also varying in time. The theoretical formulation is based on a continuum approach employing the modal superposition technique. Various cases of telescopic cranes boom are studied and the analytical results obtained in this work are tabulated in the form of dynamic response diagrams.

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