Unknown Tractions Research Articles

On interacting cracks in unidirectional fibrous composites

A crack interaction method for cracks in anisotropic fibrous composites is presented. The method is bused on the idea of superposition of resultant tractions along the crack faces. The unknown tractions are expressed by a series of base functions which describe the fundamental solution of stress induced by a solitary crack in an infinite elastic medium, loaded by any such functions. The method employed herein falls within the scope of two-dimensional elasticity but may analogously be applied to other three-dimensional problems (penny-shaped cracks). From the results of various crack configurations in unidirectional fibrous reinforced materials, it is shown that the stress intensity factors strongly depend on the axial to transverse stiffness ratio. Finally, some typical examples, which highlight specific features of the method in different composite material systems are considered and compared to other existing results.

A frictional interface contact problem in winding mechanics

Abstract The problem of frictional interface contact in winding mechanics is examined within the framework of linear two‐dimensional elasto‐statics. A model for the contact‐slip problem is used to determine the length of the slip zone and to establish the distribution of interface stresses within the stick and slip zones. The stress state in the winding mechanics is simplified by using a strip and half‐plane model. By means of integral superposition, the problem is reduced to a system of singular integral equations of the Cauchy type for the unknown normal and tangential tractions along the interface. The resulting singular integral equations are numerically solved using the Erdogan‐Gupta method.

THIN CIRCULAR PLATE UNDER TEMPERATURE LOADING IN ADHESIVE CONTACT WITH AN ELASTIC HALF-SPACE

Abstract The problem of adhesive contact between a thin circular plate under temperature loading and an isotropic elastic half-space is reduced to a problem of solving a pair of coupled integral equations for the unknown interfacial tractions. A numerical procedure for its solution is outlined and some results are presented in graphical form.

A two-dimensional theory for piezoelectric layers used in electro-mechanical transducers—I: Derivation

An Nth order two-dimensional theory is derived for strongly coupled piezoelectric layers that is suitable for use in analyzing electro-mechanical transducer response in circumstances where the field variations over the transducer face are important. Specific formulae are given for the widely used ceramic PZT-5.The first few branches of the dispersion curves for PZT-5 are obtained numerically for both the three-dimensional theory and the approximate two-dimensional theory. The correspondence of these curves at long wavelengths is used to determine a single correction factor. The face boundary conditions accommodate unknown traction and voltage so that the theory can be used in transducer applications.

The application of the extremum principles for a Bingham solid

An extension of the extremum principle concerned with statically admissible stress fields for boundary value problems of an incompressible rigid visco-plastic (Bingham) solid is derived. This extension is an inequality that gives a lower bound for the rate of work of the unknown surface tractions in certain visco-plastic boundary value problems. Lower bounds are obtained for the torque required to twist a prismatic visco-plastic bar of square crossection and these lower bounds are presented along with upper bounds obtained from an inequality that was derived in a previous paper1).

An extension of one of the extremum principles for a Bingham solid

An extension of the extremum principle concerned with velocity fields for boundary value problems of an incompressible rigid visco-plastic (Bingham) solid is derived. This extension can be used to obtain close overestimates for the rate of work of the unknown surface tractions in certain problems of visco-plastic flow.