1,721,363 research outputs found
Dynamical Analysis of Spherical Structural Elements Using the First-order Shear Deformation Theory
No full textThis lecture deals with the dynamical behaviour of hemispherical domes and shell panels. The First-order Shear Deformation Theory (FSDT) is used to analyze the above moderately thick structural elements. The treatment is conducted within the theory of linear elasticity, when the material behaviour is assumed to be homogeneous and isotropic. The governing equations of motion, written in terms of internal resultants, are expressed as functions of five kinematic parameters, by using the constitutive and the congruence relationships. The boundary conditions considered are clamped (C), simply supported (S) and free (F) edge. Numerical solutions have been computed by means of the technique known as the Generalized Differential Quadrature (GDQ) Method. These results, which are based upon the FSDT, are compared with the ones obtained using commercial programs such as Ansys, Femap/Nastran, Straus, Pro/Engineer, which also elaborate a three-dimensional analysis
Static Analysis of Functionally Graded Doubly-Curved Shells and Panels of Revolution
No full textThe Generalized Differential Quadrature (GDQ) Method is applied to study four parameter functionally graded and laminated composite shells and panels of revolution. The mechanical model is based on the so-called First-order Shear Deformation Theory (FSDT), in particular on the Toorani-Lakis Theory. The solution is given in terms of generalized displacement components of points lying on the middle surface of the shell. The generalized strains and stress resultants are evaluated by applying the Differential Quadrature rule to the generalized displacements. The transverse shear and normal stress profiles through the thickness are reconstructed a posteriori by using local three-dimensional elasticity equilibrium equations. In order to verify the accuracy of the present method, GDQ results are compared with the ones obtained with semi-analytical formulations and with 3D finite element method. A parametric study is performed to illustrate the influence of the parameters on the mechanical behavior of functionally graded shell structures made of a mixture of ceramics and metal
Vibration analysis of spherical structural elements using the GDQ method
No full textAbstractThis paper deals with the dynamical behaviour of hemispherical domes and spherical shell panels. The First-order Shear Deformation Theory (FSDT) is used to analyze the above moderately thick structural elements. The treatment is conducted within the theory of linear elasticity, when the material behaviour is assumed to be homogeneous and isotropic. The governing equations of motion, written in terms of internal resultants, are expressed as functions of five kinematic parameters, by using the constitutive and the congruence relationships. The boundary conditions considered are clamped (C), simply supported (S) and free (F) edge. Numerical solutions have been computed by means of the technique known as the Generalized Differential Quadrature (GDQ) Method. These results, which are based upon the FSDT, are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Femap/Nastran, Straus, Pro/Engineer, which also elaborate a three-dimensional analysis. The effect of different grid point distributions on the convergence, the stability and the accuracy of the GDQ procedure is investigated. The convergence rate of the natural frequencies is shown to be fast and the stability of the numerical methodology is very good. The accuracy of the method is sensitive to the number of sampling points used, to their distribution and to the boundary conditions
Free Vibrations of Three Parameter Functionally Graded Parabolic Panels of Revolution
No full textThe aim of this paper is to deal with the dynamic behaviour of moderately thick functionally
graded parabolic panels of revolution. A generalization of the power-law distribution
presented in literature is proposed. The governing equations of motion are expressed in
terms of five generalized displacement components of the points lying on the middle surface
of the parabolic shell. The Generalized Differential Quadrature (GDQ) method is used
to discretize the system equations. Numerical results concerning functionally graded parabolic
panels show the influence of the three parameters of the power-law distribution on
their mechanical behaviour
Vibration Analysis of Damaged Circular Arches with Varying Cross-section
No full textIn this paper, generalized differential quadrature
techniques are applied to the computation of the in-plane free
vibrations of thin and thick non-uniform circular arches in
undamaged and damaged configurations, when various
boundary conditions are considered. Structural damage is
represented by one crack in different positions and with
various damage levels. The crack present in a structural
member can be considered as a local stiffness reduction at the
fracturing section, which changes the dynamic behaviour of
the structure. Much effort has been devoted to dealing with
in-plane free vibration analysis of circular arches, but only a
few researchers have studied cracked circular arch structures.
The present analysis refers to the complete in-plane equations
of motion of non-uniform circular arches, in terms of
displacements and rotation. Shearing and axial deformations
as well as rotary inertia are taken into account. For given
geometric and boundary conditions, the presence of a crack
will cause displacements and rotations of sections along the
arch greater than the corresponding values resulting in an
uncracked structure. In order to evaluate the effect of cracks,
a cracked section is modelled as an elastic hinge with
rotational constant which has to simulate the local flexibility
caused by the cracked section itself. A crack will produce
discontinuities in slope of the elastic curve of the arch at the
fractured cross-section. It should be noted that in our
investigation of the in-plane dynamic response variation of
damaged arches with variable cross-section, the localized
cracks will always be considered as open
Free Vibration Analysis of Functionally Graded Panels and Shells of Revolution
No full textThe aim of this paper is to study the dynamic
behaviour of functionally graded parabolic and
circular panels and shells of revolution. The Firstorder
Shear Deformation Theory (FSDT) is used to
study these moderately thick structural elements. The
treatment is developed within the theory of linear elasticity,
when the materials are assumed to be isotropic
and inhomogeneous through the thickness direction.
The two-constituent functionally graded shell consists
of ceramic and metal that are graded through the thickness,
from one surface of the shell to the other. Two
different power-law distributions are considered for
the ceramic volume fraction. For the first power-law
distribution, the bottom surface of the structure is ceramic
rich, whereas the top surface is metal rich and
on the contrary for the second one.
The governing equations of motion are expressed
as functions of five kinematic parameters, by using
the constitutive and kinematic relationships. The solution
is given in terms of generalized displacement
components of the points lying on the middle surface
of the shell. The discretization of the system equations by means of the Generalized Differential
Quadrature (GDQ) method leads to a standard linear
eigenvalue problem, where two independent variables
are involved without using the Fourier modal expansion
methodology. Numerical results concerning eight
types of shell structures illustrate the influence of the
power-law exponent and of the power-law distribution
choice on the mechanical behaviour of parabolic and
circular shell structures
2-D Solution for Free Vibrations of Parabolic Shells Using Generalized Differential Quadrature Method
No full textThe Generalized Differential Quadrature (GDQ) procedure is developed for the free vibration analysis of complete parabolic
shells of revolution and parabolic shell panels. The First-order Shear Deformation Theory (FSDT) is used to analyze the above
moderately thick structural elements. The treatment is conducted within the theory of linear elasticity, when the material behaviour
is assumed to be homogeneous and isotropic. The governing equations of motion, written in terms of internal resultants, are
expressed as functions of five kinematic parameters, by using the constitutive and kinematic relationships. The solution is given
in terms of generalized displacement components of the points lying on the middle surface of the shell. The discretization of
the system by means of the Differential Quadrature (DQ) technique leads to a standard linear eigenvalue problem, where two
independent variables are involved. The results are obtained taking the meridional and circumferential co-ordinates into account,
without using the Fourier modal expansion methodology. Several examples of parabolic shell elements are presented to illustrate the
validity and the accuracy of GDQ method. Numerical solutions are compared with the ones obtained using commercial programs
such as Abaqus, Ansys, Femap/Nastran, Straus, Pro/Mechanica. Very good agreement is observed. Furthermore, the convergence
rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good. The accuracy of the
method is sensitive to the number of sampling points used, to their distribution and to the boundary conditions. Different typologies
of non-uniform grid point distributions are considered. The effect of the distribution choice of sampling points on the accuracy of
GDQ solution is investigated. New numerical results are presented.
© 2008 Elsevier Masson SAS. All rights reserved
Transient dynamic response of generally-shaped arches based on a GDQ-time-stepping method
No full textThis paper deals with the in-plane dynamic modeling of generally shaped arches with a varying cross-section in undamaged or damaged configuration, under different boundary conditions and external forces. The Generalized Differential Quadrature (GDQ) method is herein applied to solve numerically the problem without passing through any variational formulation, but solving directly the governing equations of motion in strong form. The main purpose of the work is to obtain a computationally efficient higher-order method for solving time integration problems. The total time interval is discretized in time steps and the GDQ method is applied to solve the initial value problem within each time step. At each time interval, a linear algebraic equation system has to be solved. A simple and efficient implementation scheme is presented. A wide GDQ-based numerical investigation is performed to study the linear dynamics of the arch with different geometries, boundary conditions and external forces. The numerical results based on the application of the GDQ method are compared with those ones provided by the Newmark method. A very good agreement is found between the two numerical approaches, which demonstrates the performance and feasibility of the proposed GDQ-time-stepping algorithm for transient dynamics
On the inclined crack problem in an orthotropic medium under biaxial loading
No full textThe problem of an inclined crack in an orthotropic medium under biaxial loading is analyzed.
A suitable coordinate transformation is introduced and two decoupled systems of the Cauchy-Riemann type are obtained in terms of complex potentials. The crack problem is solved by using the method of analytic continuation and closed form expressions of the near tip stress and displacement fields are derived.
The influence of load biaxiality on the stress intensity factors, as well as on the local stress components is studied and graphically represented. Moreover, the action of material orthotropy on various quantities describing the crack characteristic is pointed out
Strong Formulation Finite Element Method for Arbitrary Shaped Composite Structures
No full textWhen it comes to numerical methods a huge amount of methodologies and techniques comes out. Since several researchers throughout all the past decades tried a better way to solve different problems in engineering. It can be pointed out that most of the numerical approaches hitherto proposed can be simply classified as based on two different formulations. Engineers in several branches know that physical problems can be mathematically solved, generally, using a system of partial differential equations. Since analytical solutions for these problems are usually limited to very simple cases numerical techniques must be employed in order to find an approximate solution for these problems. Historically speaking two approaches have been followed. On one hand the system is directly discretized using the so-called collocation methods based on the distribution of points upon the physical domain. On the other hand variational or weak formulations find an approximate solution evaluating the equations in their weakened form. As it is generally known collocation methods are global and use polynomials of high degree for approximating the unknown field, whereas domain decomposition techniques, such as the Finite Element Method (FEM), decompose the domain in several subdomains evaluating several local solutions which are related by the assembly. The aim of this work is to present several methods under the heading of SFEM (Strong Formulation Finite Element Method). Since a strong formulation, analogous to the collocation approach, is coupled with a domain decomposition technique, proper of the FEM. In this way the standard FEM could be termed WFEM. Due to the fact that it is based on the weak formulation and in opposition to SFEM, which is based on the strong formulation. Summarizing the main contributions are the general view in which strong formulation methods could be presented and the introduction of the mapping technique (generally connected to the FEM) for the solution of arbitrary shaped elements without introduction a variational form of the differential system, but solving it directly. Convergence, stability, accuracy and reliability of the SFEM are illustrated varying the principal parameters of this approach and comparing them to WFEM. Thus varying the number of points, the point location, the basis functions and the number of elements it is possible to observe the numerical behaviour of the SFEM
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