Static analysis of shear-deformable shells of revolution via G.D.Q. method

Erasmo Viola,Edoardo Artioli 국제구조공학회 2005 Structural Engineering and Mechanics, An Int'l Jou Vol.19 No.4

This paper deals with a novel application of the Generalized Differential Quadrature (G.D.Q.) method to the linear elastic static analysis of isotropic rotational shells. The governing equations of equilibrium, in terms of stress resultants and couples, are those from Reissner-Mindlin shear deformation shell theory. These equations, written in terms of internal-resultants circular harmonic amplitudes, are first put into generalized displacements form, by use of the strain-displacements relationships and the constitutive equations. The resulting systems are solved by means of the G.D.Q. technique with favourable precision, leading to accurate stress patterns.

The G. D. Q. method for the harmonic dynamic analysis of rotational shell structural elements

Viola, Erasmo,Artioli, Edoardo Techno-Press 2004 Structural Engineering and Mechanics, An Int'l Jou Vol.17 No.6

This paper deals with the modal analysis of rotational shell structures by means of the numerical solution technique known as the Generalized Differential Quadrature (G. D. Q.) method. The treatment is conducted within the Reissner first order shear deformation theory (F. S. D. T.) for linearly elastic isotropic shells. Starting from a non-linear formulation, the compatibility equations via Principle of Virtual Works are obtained, for the general shell structure, given the internal equilibrium equations in terms of stress resultants and couples. These equations are subsequently linearized and specialized for the rotational geometry, expanding all problem variables in a partial Fourier series, with respect to the longitudinal coordinate. The procedure leads to the fundamental system of dynamic equilibrium equations in terms of the reference surface kinematic harmonic components. Finally, a one-dimensional problem, by means of a set of five ordinary differential equations, in which the only spatial coordinate appearing is the one along meridians, is obtained. This can be conveniently solved using an appropriate G. D. Q. method in meridional direction, yielding accurate results with an extremely low computational cost and not using the so-called "delta-point" technique.

The G. D. Q. method for the harmonic dynamic analysis of rotational shell structural elements

Edoardo Artioli,Erasmo Viola 국제구조공학회 2004 Structural Engineering and Mechanics, An Int'l Jou Vol.17 No.6

Static analysis of shear-deformable shells of revolution via G.D.Q. method

Artioli, Edoardo,Viola, Erasmo Techno-Press 2005 Structural Engineering and Mechanics, An Int'l Jou Vol.19 No.4

This paper deals with a novel application of the Generalized Differential Quadrature (G.D.Q.) method to the linear elastic static analysis of isotropic rotational shells. The governing equations of equilibrium, in terms of stress resultants and couples, are those from Reissner-Mindlin shear deformation shell theory. These equations, written in terms of internal-resultants circular harmonic amplitudes, are first put into generalized displacements form, by use of the strain-displacements relationships and the constitutive equations. The resulting systems are solved by means of the G.D.Q. technique with favourable precision, leading to accurate stress patterns.

Effect of boundary conditions on the stability of beams under conservative and non-conservative forces

Marzani, Alessandro,Viola, Erasmo Techno-Press 2003 Structural Engineering and Mechanics, An Int'l Jou Vol.16 No.2

This paper, which is an extension of a previous work by Viola et al. (2002), deals with the dynamic stability of beams under a triangularly distributed sub-tangential forces when the effect of an elastically restrained end is taken into account. The sub-tangential forces can be realised by a combination of axial and tangential follower forces, that are conservative and non-conservative forces, respectively. The studied beams become unstable in the form of either flutter or divergence, depending on the degree of non-conservativeness of the distributed sub-tangential forces and the stiffness of the elastically restrained end. A non-conservative parameter ${\alpha}$ is introduced to provide all possible combinations of these forces. Problems of this kind are usually, at least in the first approximation, reduced to the analysis of beams according to the Bernoulli-Euler theory if shear deformability and rotational inertia are negligible. The equation governing the system may be derived from the extended form of Hamilton's principle. The stability maps will be obtained from the eigenvalue analysis in order to define the divergence and flutter domain. The passage from divergence to flutter is associated with a noticeable lowering of the critical load. A number of particular cases can be immediately recovered.

Active shape change of an SMA hybrid composite plate

Daghia, Federica,Inman, Daniel J.,Ubertini, Francesco,Viola, Erasmo Techno-Press 2010 Smart Structures and Systems, An International Jou Vol.6 No.2

An experimental study was carried out to investigate the shape control of plates via embedded shape memory alloy (SMA) wires. An extensive body of literature proposes the use of SMA wires to actively modify the shape or stiffness of a structure; in most cases, however, the study focuses on modeling and little experimental data is available. In this work, a simple proof of concept specimen was built by attaching four prestrained SMA wires to one side of a carbon fiber laminate plate strip. The specimen was clamped at one end and tested in an environmental chamber, measuring the tip displacement and the SMA temperature. At heating, actuation of the SMA wires bends the plate; at cooling deformation is partially recovered. The specimen was actuated a few times between two fixed temperatures $T_c$ and $T_h$, whereas in the last actuation a temperature $T_f$ > $T_h$ was reached. Contrary to most model predictions, in the first actuation the transformation temperatures are significantly higher than in the following cycles, which are stable. Moreover, if the temperature $T_h$ is exceeded, two separate actuations occur during heating: the first follows the path of the stable cycles; the second, starting at $T_h$, is similar to the first cycle. An interpretation of the phenomenon is given using some differential scanning calorimeter (DSC) measurements. The observed behavior emphasizes the need to build a more comprehensive constitutive model able to include these effects.

Active shape change of an SMA hybrid composite plate

Federica Daghia,Daniel J. Inman,Francesco Ubertini,Erasmo Viola 국제구조공학회 2010 Smart Structures and Systems, An International Jou Vol.6 No.2

An experimental study was carried out to investigate the shape control of plates via embedded shape memory alloy (SMA) wires. An extensive body of literature proposes the use of SMA wires to actively modify the shape or stiffness of a structure; in most cases, however, the study focuses on modeling and little experimental data is available. In this work, a simple proof of concept specimen was built by attaching four prestrained SMA wires to one side of a carbon fiber laminate plate strip. The specimen was clamped at one end and tested in an environmental chamber, measuring the tip displacement and the SMA temperature. At heating, actuation of the SMA wires bends the plate; at cooling deformation is partially recovered. The specimen was actuated a few times between two fixed temperatures Tc and Th, whereas in the last actuation a temperature Tf > Th was reached. Contrary to most model predictions, in the first actuation the transformation temperatures are significantly higher than in the following cycles, which are stable. Moreover, if the temperature Th is exceeded, two separate actuations occur during heating: the first follows the path of the stable cycles; the second, starting at Th, is similar to the first cycle. An interpretation of the phenomenon is given using some differential scanning calorimeter (DSC) measurements. The observed behavior emphasizes the need to build a more comprehensive constitutive model able to include these effects.