James Ting-Shun Wang

Interlaminar Stresses in Symmetric Composite Laminates

Interlaminar stresses and displacements of each layer satisfying geo metrical boundary conditions are represented in series of Legendre poly nomials. The extended Galerkin procedure is used for each layer, and the final solutions are obtained by requiring the satisfaction of continuity conditions at each interface and the stress boundary conditions at exterior planes. A computer program has been prepared, and numerical results are presented and compared with existing data.

Local buckling of delaminated composite sandwich plates

A two-dimensional model of the delaminated face sheet of sandwich plates for predicting local huckling using continuous analysis is presented. The analysis procedure can handle without difficulty sandwich plates having single or multiple embedded delaminations of various shapes and sizes at any locations. The continuous analysis treats the delamination between a face sheet and the core as a continuous system of a perfectly bonded laminate on the core but with an added fictitious force system to make interfacial tractions to vanish over the delaminated region. The method presented in the study is straightforward, simple, and accurate for determining the buckling load of delaminated sandwich plates. A number of numerical results accounting for the effects of transverse normal and shear stiffnesses of the core on the buckling load of sandwich plates having delaminations of various shapes and sizes at different locations are presented. The illustrative examples indicate that the present method is effective and useful for practical applications.

On the Solution of Plates of Composite Materials

In the analysis of anisotropic plates, the twist-coupling terms involving Dls and D26 are generally neglected in prescribing the simply supported boundary conditions and may be referred to many papers and reports such as [1]. Recent attempts [2] were made for the determination of buckling loads of rectangular homogeneous anisotropic plates of composite materials where the moment curvature relations involve mixed derivatives of the transverse displacement with respect to x and y. Deformation surfaces assumed in double Fourier series were used in conjunction with Lagrange multipliers method [3,4] in the energy formulation of the problems. The analysis yields excellent results for completely clamped plates. However, the assumed series diverges for simply supported plates. A double power series solution was then used and the assumed

Axisymmetric vibration of hemispherical shells.

The axisymmetric dynamic response of hemispherical shells subjected to arbitrary loading is formulated according to elastic bending theory of shells. Generalized Greens functions are constructed, and closed form solutions are obtained for hemispherical shells having roller-hinged and roller-clamped edges. The results can be reduced to the solutions obtained by other authors according to membrane shell theory. Comparison is made of the frequencies obtained according to the present bending theory and the frequencies based on membrane theory. When harmonic loadings are applied along the edge of roller-hinged and along the edge of roller-clamped shells, the frequency equations for a shell with hinged edge and a shell completely clamped along its edge are obtained. The lowest three frequencies for a fixed-edge hemispherical shell are calculated for three different thickness-radius ratios.

Energy Release Rate of Double Beam-Plates with Repairing Elements

An engineering analysis for determining the strain energy release rate of symmetrically loaded double beam-plates with repairing or reinforcing elements in the transverse direction which are densely distributed across the width in the disbond regions is presented. The concept of strain energy release rate evaluated by computing the rate of energy released from the disbond front has been verified to be exactly the same and simpler to use than the most referenced work of Kanninen by differentiation of the total strain energy of the entire system with respect to the disbond length. Due to the simplicity of the new concept for determining the strain energy release rate, it allows one to derive the exact analytical solutions for double beam-plates containing repair or reinforce elements and satisfying continuity at the delamination front as well as boundary conditions at both ends of the system. Some comparisons of the strain energy release rate for double beam-plates without repair elements to other approximations are also made. Each side of a double beam-plate system in the perfect segment is modeled as a beam-plate on an elastic foundation, while disbond segments are treated as beam-plates under transverse loading and constrained by repairing or reinforcing elements as axially loaded members at discrete points. Some numerical results for a double cantilever beam-plate with one and two rows of reinforcing elements under end loads are presented for illustrating the procedure as well as for future reference. The general concept and analysis procedure should be applicable to other structural systems and for mixed-mode delaminations.

On the Method of Continuous Analysis

The paper, summarizing studies presented in seven journal papers using the method of continuous analysis, is written to honor Professor Y.H. Pao of the Institute of Applied Mechanics at the National Taiwan University on his seventieth birthday for his many significant contributions and leadership in the field of mechanics. These seven papers contain investigations concerning stress, buckling, and vibration analyses of beams and plates having disbonds. The authors feel privileged to have this opportunity to join with Professor Paos many friends, colleagues and students to participate in this joyous occasion. Being able to appear in this prestigious special issue of the Chinese Journal of Mechanics, the authors believe that the spread of each of the seven papers in the structural mechanics community must at least be increased by ten fold. Hence, the numbering of the reference papers is amplified by a factor of ten which amounts to a total number of seventy as being used in the listing of papers under References. We use this number of seventy to wish Professor Y.H. Pao to have many happy returns on his seventieth birthday.

Use of a Direct Boundary Element Method for Pin-Loaded Plates

A previously developed direct boundary element method for analyzing stresses around pin-loaded holes of compositelaminates hasbeen extended witha ree ned and improved computationalalgorithm. Themethod,procedure, and computer program are verie ed by elasticity solutions in polar coordinates for eyebars and plates having an open, as well as loaded, hole. In turn, boundary tractions generated by the direct boundary element method allowing direct application of elasticity solutions are presented. Such a scheme, which couples the boundary element and analytical methods, appears to be plausible, accurate, and efe cient for practical applications.