Some Remarks on the Numerical Solution of a Strain Gradient Plasticity Theory

A Semi-analytical Solution for Flexural Vibration of Micro Beams Based on the Strain Gradient Theory

In this paper, the flexural free vibrations of three dimensional micro beams are investigated based on strain gradient theory. The most general form of the strain gradient theory which contains five higher-order material constants has been applied to the micro beam to take the small-scale effects into account. Having considered the Euler-Bernoulli beam model, governing equations of motion are w...

Some links between Cosserat, strain gradient crystal plasticity and the statistical theory of dislocations

Static analysis of rectangular nanoplates using exponential shear deformation theory based on strain gradient elasticity theory

In this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. For this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. From the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried...

Some Remarks on Number Theory

This note contains some disconnected minor remarks on number theory . 1 . Let (1) Iz j I=1, 1<j<co be an infinite sequence of numbers on the unit circle . Put n s(k, n) _ z~, Ak = Jim sup I s(k, n) j=1 k=oo and denote by B k the upper bound of the numbers I s(k,n)j . If z j = e 2nij' a =A 0 then all the Ak 's are finite and if the continued fraction development of a has bounded denominators the...

Some Remarks on Set Theory

Let there be given n ordinals cti, alt • • • , an. It is well known that every ordinal can be written uniquely as the sum of indecomposable ordinals. (An ordinal is said to be indecomposable if it is not the sum of two smaller ordinals.) Denote by (ct...