THE appearance of a treatise in English upon the mathematical theory of elasticity is an event the potential importance of which may be judged by the that the author, in his frequent suggestions for collateral reading, refers to only three such, those of Southwell, Timoshenko, and Love. In spirit and content Sokolnikoff}s book differs greatly from each and all of these. It may be described by a possible sub-title: “A pure mathematician surveys topics related to certain problems in the mathematical theory of elasticity”. It is symptomatic of the change in outlook of American mathematics over the past few decades. Mathematical Theory Of Elasticity Prof. I. S. Sokolnikoff with the collaboration of Asst. Prof. R. D. Speche. Pp. xi + 373. (New York and London: McGraw-Hill Book Co., Inc., 1946.) 22s. 6d.

Mathematical Theory Of Elasticity

A review of the recent developments in the analysis of laminated beams and plates with an emphasis on shear effects and buckling is presented. A discussion of various shear-deformation theories for plates and beams is given. The available theories are derived assuming a variation of either the in-plane displacement components or the stress components or both in the thickness coordinate. A review of the recently developed finite elements to analyze thin and thick laminated beams and plates is given next. These elements have been derived using the displacement methods, or the mixed methods or the hybrid methods. Recent studies on the buckling and postbuckling behavior of perfect and geometrically imperfect plates are described next. These behaviors have been studied using analytical, numerical, and experimental techniques. Finally, a review of the various studies on the delamination buckling and growth in beams and plates is given. Once again, the studies have been conducted using analytical, numerical, and experimental techniques. The energy release rates have been determined using closed-form solutions or using numerical differentiation. Mention also is made of studies on multiple delaminations and on dynamic response of composite laminates under impact loads.

Recent advances in analysis of laminated beams and plates. Part I - Sheareffects and buckling.

Effective elastic properties of periodic hexagonal honeycombs

Effective stress-strain relations for two-dimensional cellular sandwich cores: Homogenization, material models, and properties

Assessment of continuum models for sandwich panel honeycomb cores

Four computational simulation methods with different levels of sophistication were used to simulate thermal behavior and structural changes of composite sandwich panels with a honeycomb core subjected to a variety of environmental effects. The models on thich these methods are based include three-dimensional finite-element modeling, three-dimensional finite-element modeling assuming a homogeneous core, laminate theory, and simple equations for predicting the equivalent properties of the honeycomb core. A procedure was developed and embedded in a composite mechanics computer code, which made it possile to conduct parametric studies to determine 'optimum' composite sandwich configurations for specific applications. The procedure was applied for the evaluation of composite sandwich behavior at the global, local, laminate, ply, and micromechanics levels when the composite sandwich is subjected to hygral, thermal, and mechanical loading environments.

/pdf/fiber-composite-sandwich-thermostructural-behavior-4ogqmib04z.pdf

Fiber Composite Sandwich Thermostructural Behavior: Computational Simulation

https://ntrs.nasa.gov/api/citations/19920012984/downloads/19920012984.pdf

Improved accuracy for finite element structural analysis via an integrated force method

The installation and use of a computer code, COBSTRAN (COmposite Blade STRuctrual ANalyzer), developed for the design and analysis of composite turbofan and turboprop blades and also for composite wind turbine blades was described. This code combines composite mechanics and laminate theory with an internal data base of fiber and matrix properties. Inputs to the code are constituent fiber and matrix material properties, factors reflecting the fabrication process, composite geometry and blade geometry. COBSTRAN performs the micromechanics, macromechanics and laminate analyses of these fiber composites. COBSTRAN generates a NASTRAN model with equivalent anisotropic homogeneous material properties. Stress output from NASTRAN is used to calculate individual ply stresses, strains, interply stresses, thru-the-thickness stresses and failure margins. Curved panel structures may be modeled providing the curvature of a cross-section is defined by a single value function. COBSTRAN is written in FORTRAN 77.

Composite blade structural analyzer (COBSTRAN) user's manual

Several computational levels of progressive sophistication/simplification are described to computationally simulate composite sandwich hygral, thermal, and structural behavior. The computational levels of sophistication include: (1) three-dimensional detailed finite element modeling of the honeycomb, the adhesive and the composite faces; (2) three-dimensional finite element modeling of the honeycomb assumed to be an equivalent continuous, homogeneous medium, the adhesive and the composite faces; (3) laminate theory simulation where the honeycomb (metal or composite) is assumed to consist of plies with equivalent properties; and (4) derivations of approximate, simplified equations for thermal and mechanical properties by simulating the honeycomb as an equivalent homogeneous medium. The approximate equations are combined with composite hygrothermomechanical and laminate theories to provide a simple and effective computational procedure for simulating the thermomechanical/thermostructural behavior of fiber composite sandwich structures.

Structural and dynamic analyses are presented for a shroudless, hollow titanium fan blade proposed for future use in aircraft turbine engines. The blade was modeled and analyzed using the composite blade structural analysis computer program (COBSTRAN); an integrated program consisting of mesh generators, composite mechanics codes, NASTRAN, and pre- and post-processors. Vibration and impact analyses are presented. The vibration analysis was conducted with COBSTRAN. Results show the effect of the centrifugal force field on frequencies, twist, and blade camber. Bird impact analysis was performed with the multi-mode blade impact computer program. This program uses the geometric model and modal analysis from the COBSTRAN vibration analysis to determine the gross impact response of the fan blades to bird strikes. The structural performance of this blade is also compared to a blade of similar design but with composite in-lays on the outer surface. Results show that the composite in-lays can be selected (designed) to substantially modify the mechanical performance of the shroudless, hollow fan blade.

/pdf/structural-dynamics-of-shroudless-hollow-fan-blades-with-1qwyk7nxl9.pdf

Structural dynamics of shroudless, hollow fan blades with composite in-lays

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Fiber Composite Sandwich Thermostructural Behavior: Computational Simulation

Improved accuracy for finite element structural analysis via an integrated force method

Composite blade structural analyzer (COBSTRAN) user's manual

Fiber Composite Sandwich Thermostructural Behavior: Computational Simulation

Structural dynamics of shroudless, hollow fan blades with composite in-lays