Dynamic Behavior of a Cylindrical Shell with a Liquid under the Action of Nonstationary Pressure Wave

The problem of axisymmetric hydroelastic deformation of a thin cylindrical shell containing a liquid under the action of a moving load is approximately solved. It is reduced to the equation of bending of the shell and the condition of incompressibility of the liquid in the cylinder. The deflections of the shell and the level of lowering of the liquid are unknown. For solution, the Galerkin method is used and the problem is reduced to a system of nonlinear algebraic equations. A simpler solution is considered without taking into account the incompressibility condition. Here, in addition to the deformed state of the shell, the critical speeds of the moving load are determined analytically.

Local null controllability of the penalized Boussinesq system with a reduced number of controls

<p style='text-indent:20px;'>In this paper we consider the Boussinesq system with homogeneous Dirichlet boundary conditions, defined in a regular domain <inline-formula><tex-math id="M1">\begin{document}$ \Omega\subset\mathbb R^N $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M2">\begin{document}$ N = 2 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ N = 3 $\end{document}</tex-math></inline-formula>. The incompressibility condition of the fluid is replaced by its approximation by penalization with a small parameter <inline-formula><tex-math id="M4">\begin{document}$ \varepsilon &gt; 0 $\end{document}</tex-math></inline-formula>. We prove that our system is locally null controllable using a control with a restricted number of components, localized in an open set <inline-formula><tex-math id="M5">\begin{document}$ \omega $\end{document}</tex-math></inline-formula> contained in <inline-formula><tex-math id="M6">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula>. We also show that the control cost is bounded uniformly with respect to <inline-formula><tex-math id="M7">\begin{document}$ \varepsilon \rightarrow 0 $\end{document}</tex-math></inline-formula>. The proof is based on a linearization argument. The null controllability of the linearized system is obtained by proving a new Carleman estimate for the adjoint system. This inequality is derived by exploiting the coercivity of some second order differential operator involving crossed derivatives.</p>

Analysis and Calculation of the Art of Internal High Pressure Forming

nternal high pressure forming is a new technology producing hollow light components. Due to the process of internal high pressure forming is very complicated with many factors, the dissertation will focus on the use of plastic-elastic force theory to acquire the hydraulic pressure needed and the tubes wall thickness in the final forming fillet. Based on the assumption of volume's incompressibility condition, we analyze and calculate the stress and strain of the tubes wall. Finally we estimate the formula of the hydraulic pressure needed in the forming process. The whole work can offer a concise formula to engineer in the infancy of designing. And it also is the great theoretical support to the development of the internal high pressure forming.

On Diffusion Through Soft Filter

Diffusion through soft polymer filters is a nonlinear process: the increase of the pressure on the filtrating liquid does not trigger the proportional increase of the flux through the filter. There are two sources of nonlinearity: the diffusivity properties of the filter and its high deformability. In the present work we use a theoretical formulation coupling large deformations and diffusion to describe a liquid flux through a polymeric filter. Two key factors making the present formulation simple are the molecular incompressibility condition and the nonlinear mobility tensor. The developed model is calibrated based on the experiments on toluene-rubber filtration.

Nonlinear Periodic Oscillation of a Cylindrical Microvoid Centered at an Isotropic Incompressible Ogden Cylinder

We study the dynamic mathematical model for an infinitely long cylinder composed of an isotropic incompressible Ogden material with a microvoid at its center, where the outer surface of the cylinder is subjected to a uniform radial tensile load. Using the incompressibility condition and the boundary conditions, we obtain a second-order nonlinear ordinary differential equation that describes the motion of the microvoid with time. Qualitatively, we find that this equation has two types of solutions. One is a classical nonlinear periodic solution which describes that the motion of the microvoid is a nonlinear periodic oscillation; the other is a blow-up solution. Significantly, for the isotropic incompressible Ogden material, there exist some special values of material parameters, the phase diagrams of the motion equation have homoclinic orbits, which means that the amplitude of a nonlinear periodic oscillation increases discontinuously with the increasing load.

Anisotropic Tensile Deformation of Lotus-Type Porous Copper

The tensile deformation of lotus-type porous copper with cylindrical pores oriented in one direction was investigated. Deformation was occured homogeneously in the copper matrix for loadings parallel to the orientation direction of pores (pore direction), while deformation was localized in the matrix around pores for loadings perpendicular to the pore direction. In the case of parallel loading the decrease in cross section of tensile specimen was smaller than that of nonporous copper, because of the constant-volume law (i.e. incompressibility condition) for deformation was not applicable to the deformation of pores. In the case of perpendicular loading, the deformed regions were disconnected and constant-volume law holds only in the matrix around the pores, and thus, the cross section hardly decreases during the tensile deformation.

Generalized Framework for Three-Dimensional Upper Bound Limit Analysis in a Tresca Material

A new method is proposed for deriving kinematically admissible velocity fields (KAVFs) for three-dimensional upper bound limit analyses in a Tresca material using coordinate transformations. The method allows the incompressibility condition to be satisfied simply by imposing certain requirements on the analytical form of velocity magnitudes. This allows for new classes of velocity fields to be derived solely using standard procedures. These new classes of fields include: KAVFs with new streamline shapes; new planar but non-plane-strain KAVFs; new radial but nonaxisymmetric KAVFs. The method allows the expression of local dissipation of plastic work in any field to be derived in a closed form. The proposed method makes an attempt to expand the applicability of three-dimensional upper bound limit analysis by introducing more realistic shapes of KAVFs, while maintaining simplicity and clear engineering meaning.

Morphometry and strain distribution of the C57BL/6 mouse aorta

The goal of the present study was to obtain a systematic set of data along the length of the mouse aorta to study variations of morphometry (diameter, wall thickness, and curvature), strain, and stress of the mouse aorta. Five mice were imaged with a 13-MHz ultrasound probe to determine the in vivo diameter along the aorta. A cast was made of these aortas to validate the ultrasonic diameter measurements. The root mean squared and systematic errors for these measurements were 12.6% and 6.4% of the mean ultrasound diameter, respectively. The longitudinal variations of geometry, stress, and strain from the aortic valve to the common iliac bifurcation were documented. Our results show that the residual circumferential strain leads to a uniformity of transmural strain of the aorta in the loaded state along the entire length of the aorta. Furthermore, we validated the incompressibility condition along the length of the aorta. These data of normal mice will serve as a reference state for the study of disease in future knockout models.

Equations relating structure functions of all orders

Exact equations are given that relate velocity structure functions of arbitrary order with other statistics. ‘Exact’ means that no approximations are used except that the Navier–Stokes equation and incompressibility condition are assumed to be accurate. The exact equations are used to determine the structure function equations of all orders for locally homogeneous but anisotropic turbulence as well as for the locally isotropic case. The uses of these equations for investigating the approach to local homogeneity as well as to local isotropy and the balance of the equations and identification of scaling ranges are discussed. The implications for scaling exponents and investigation of intermittency are briefly discussed.