Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates

The accuracy of certain thick plate elements when used in the context of thin plate problems can be improved by the use of reduced integration of the stiffness matrices. A series of numerical experiments on five different quadrilateral thick plate elements demonstrates the use of reduced integration and indicates the main reason for its success. This is the relaxation of a constraint on the shear strains. It is shown that the performance of a nine-noded Lagrangian element is near optimal.

A study of quadrilateral plate bending elements with ‘reduced’ integration

https://www.civil.iitb.ac.in/~tkant/papers/TKant-IITB-JP057.pdf

A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches

Forced motions of laminated composite plates are investigated using a finite element that accounts for the transverse shear strains, rotary inertia, and large rotations (in the von Karman sense). The present results when specialized for isotropic plates are found to be in good agreement with those available in the literature. Numerical results of the nonlinear analysis of composite plates are presented showing the effects of plate thickness, lamination scheme, boundary conditions, and loading on the deflections and stresses. The new results for composite plates should serve as bench marks for future investigations. mation are assumed to remain straight and normal to the midsurface after deformation (i.e., transverse shear strains are zero), has been used to calculate frequencies, static response, and dynamic response under applied loads. Recent studies in the analysis of plates have shown that the effect of the transverse shear strains on the static and dynamic response of plates is significant. For example, the natural frequencies of vibration predicted by the classical plate theory are 25% higher, for plate side-to-thickness ratio of 10, than those predicted by a shear deformation theory (SDT). In transient analysis of plates the classical plate theory predicts unrealistically large phase velocities in the plate for shorter wavelengths. The Timoshenko beam theory,3 which includes transverse shear and rotary inertia effects, has been extended to isotropic plates by Reissner 4'5 and Mindlin,6 and to laminated anisotropic plates by Yang et al.7 A generalization of the von Karman nonlinear plate theory for isotropic plates to include the effects of transverse shear and rotary inertia in the theory of orthotropic plates is due to Medwadawski,8 and that for anisotropic plates is due to Ebcioglu.9 With the increased application of advanced fiber composite material to jet engine fan or compressor blades, and in high performance aircraft, studies involving transient response of plates made of such materials are needed to assess the capability of these materials to withstand the forces of impact due to foreign objects (e.g., the ingestion of stones, nuts and bolts, hailstones, or birds in jet engines). Previous in- vestigations into the linear transient analysis of composite plates include Moon's10'11 investigation of the response of infinite laminated plates subjected to transverse impact loads at the center of the plate; Chow's12 study of laminated plates (with transverse shear and rotary inertia) using the Laplace transform technique; the Wang et al. 13 investigation, by the method of characteristi cs, of unsymmetrical orthotropic laminated plates; and Sun and Whitney's14'15 study of plates under cylindrical bending. More recently, the present author16'17 investigated the linear transient response of layered anisotropic composite rectangular plates and presented extensive numerical results for center deflection and stresses.

Geometrically nonlinear transient analysis of laminated composite plates

Finite element transient dynamic analysis of isotropic and fibre reinforced composite plates using a higher-order theory

: The condition of stability of the finite-difference equation for the transient response of a 'moderately thick' plate is derived. The effect of transverse shear and rotatory inertia on the stability condition are examined. For the same size of space increment the stability condition for a moderately thick plate requires a much smaller time increment than the corresponding one for a 'thin' plate in order to insure numerical stability. It is found that when either the effect of transverse shear or rotatory inertia is included, the sufficient stability condition is identical to that for the thin plate. (Author)

Stability of transient solution of moderately thick plate by finite-difference method

The dynamic stability of an axially-stiffened cylinder under an axial impulsive load in the form of a step function is investigated. Donnell-Karman-type nonlinear equations are derived for the initially imperfect stiffened cylinders including eccentricity of stiffeners. A buckling criterion is defined and buckling loads are computed for different imperfection parameters and positive and negative eccentricities for a cylinder with an axial stiffening system. The results indicate the high imperfection sensitivity of axially-stiffened cylinders.

Dynamic Stability of Axially-Stiffened Imperfect Cylindrical Shells under Axial Step Loading

The dynamic stability of ring stiffened cylindrical shells under axial and lateral step loads is investigated. The effects of initial geometric imperfection and the eccentricity of the stiffeners on the dynamic buckling loads of the shell are determined. Studies show that ring-stiffened cylinders are imperfection-sensitive and can buckle at a load considerably smaller than that predicted for perfect shells. The study also demonstrated that the essential mechanism for the imperfection sensitivity in the dynamic range is the so-called "column" asymmetric mode withm = 1 andn> >l.

Dynamic buckling of ring stiffened cylindrical shells

Influence of damping on the dynamic stability of spherical caps under step pressure loading

Theme T paper considers the transient response of a circular cylindrical panel to arbitrary time-dependent loads. The study is based on the improved shell theory which includes effects of transverse shear and rotatory inertias. The governing equations of motion are solved by an explicit numerical procedure. Results are obtained for panels subjected to a timevarying normal load uniformly distributed over the entire panel surface. They are compared with findings based on the classical shell theory. Noteworthy differences between the two theories are obtained.

Tien-Yu Tsui

Papers

Stability of transient solution of moderately thick plate by finite-difference method

Dynamic Stability of Axially-Stiffened Imperfect Cylindrical Shells under Axial Step Loading

Dynamic buckling of ring stiffened cylindrical shells

Influence of damping on the dynamic stability of spherical caps under step pressure loading

Dynamic Response of Moderately Thick Cylindrical Panels