Introduction. 1. Nonlinear theories of elasticity of plates and shells 2. Nonlinear theories of doubly curved shells for conventional and advanced materials 3. Introduction to nonlinear dynamics 4. Vibrations of rectangular plates 5. Vibrations of empty and fluid-filled circular cylindrical 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells 9. Vibrations of circular cylindrical panels with different boundary conditions 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials 11. Meshless discretization of plates and shells of complex shapes by using the R-functions 12. Vibrations of circular plates and rotating disks 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads 14. Nonlinear stability and vibrations of circular shells conveying flow 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.

/pdf/nonlinear-vibrations-and-stability-of-shells-and-plates-4zhg0tiabh.pdf

Nonlinear Vibrations and Stability of Shells and Plates

1 Formulation of the equations of motion 2 Element energy functions 3 Introduction to the finite element displacement method 4 In-plane vibration of plates 5 Vibration of solids 6 Flexural vibration of plates 7 Vibration of stiffened plates and folded plate structures 8 Vibration of shells 9 Vibration of laminated plates and shells 10 Hierarchical finite element method 11 Analysis of free vibration 12 Forced response 13 Forced response II 14 Computer analysis technique

Introduction to finite element vibration analysis

The response of hexagonal, metallic honeycomb to in-plane compressive loading is studied through a combination of experiment and analysis. This material with periodic microstructure has a load-displacement response characterized by a relatively sharp initial rise to a load maximum followed by an extended load plateau which is terminated by a sharp rise in load. In the first part of the response, the material deforms essentially in a uniform fashion (stable). Following the load maximum, deformation tends to localize to one row of cells which collapses at a dropping overall load until the walls of each cell come into contact. Contact arrests further deformation in the collapsed row of cells and causes spreading of deformation in the adjacent rows. Under displacement-controlled loading, this row by row collapse can continue, with relatively small changes in the required load, until the whole specimen is collapsed. The load required for further crushing increases sharply beyond this point. This process has been reproduced through large-scale numerical simulations of the problem. In addition, we show how the local response of the material, obtained from a compression test on a representative microsection, can be used to establish the elastic properties, the load at the onset of instability, and the stress level at which deformation propagates from row to row. The local response is subsequently used to study the problem parametrically.

In-plane compressive response and crushing of honeycomb

Membrane filtration has become firmly established as a primary technology for ensuring the purity, safety and/or efficiency of the treatment of water or effluents. In this paper, we review the improvements that have been achieved concerning the membranes used for microfiltration, ultrafiltration, nanofiltration/reverse osmosis processes during the last decades. More especially, we review the state of the art computational fluid dynamics (CFD) methods applied to membranes processes. Many studies have focused on the best ways of using a particular membrane process. But, the design of new membrane systems requires a considerable amount of process development as well as robust methods. Computational fluid dynamics may provide a lot of interesting information for the development of membrane processes. We review the different ways in which CFD methods are used to improve membrane performance.

Computational fluid dynamics applied to membranes: State of the art and opportunities

An exact solution to the Navier–Stokes equations for the flow in a channel or tube with an accelerating surface velocity is presented. By means of a similarity transformation the equations of motion are reduced to a single ordinary differential equation for the similarity function which is solved numerically. For the two-dimensional flow in a channel, a single solution is found to exist when the Reynolds number R is less than 310. When R exceeds 310, two additional solutions appear and form a closed branch connecting two different asymptotic states at infinite R. The large R structure of the solutions consists of an inviscid fluid core plus an O(R−1) thin boundary layer adjacent to the moving wall. Matched-asymptotic-expansion techniques are used to construct asymptotic series that are consistent with each of the numerical solutions.For the axisymmetric non-swirling flow in a tube, however, the situation is quite different. For R [Lt ] 10[sdot ]25, two solutions exist which form a closed branch. Beyond 10[sdot ]25, no similarity solutions exist within the range 10[sdot ]25 0. These solutions, however, do not evolve from the R = 0 state nor do they bifurcate from the non-swirling solutions at any finite value of R.

Steady flow in a channel or tube with an accelerating surface velocity. An exact solution to the Navier—Stokes equations with reverse flow

The flow in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted is considered. Following Berman, a solution is obtained giving a fourth-order non-linear differential equation which depends on a suction Reynolds number R. Numerical solutions of this equation have been obtained. Series solutions of this equation for small and large Reynolds number are given and are shown to give good agreement with the numerical solutions.

Laminar Flow in a Uniformly Porous Channel

Large amplitude flexural vibration of rectangular plates

Vibration of Stiffened Plates

The vibration of circular plates when the amplitude is large is governed by nonlinear partial differential equations. An approximate formulation of these equations for the static case has previously been proposed by H. M. Berger. These equations are here extended to the dynamic case. A simplification in the statement of the problem is introduced by requiring that the in-plane displacement at the boundary of the plate vanish. A modified Galerkin procedure is then used for solving the resulting equations. It is shown that for both simply supported and clamped circular plates the vibration can be expressed in terms of elliptic functions. Numerical results are given for the calculation of frequencies and stresses. A method is suggested for solving forced vibration problems.

Thein Wah

Papers

Laminar Flow in a Uniformly Porous Channel

Large amplitude flexural vibration of rectangular plates

Vibration of Stiffened Plates

Vibration of Circular Plates at Large Amplitudes

Buckling of thin circular rings under uniform pressure