# Applied Mathematics and Mechanics

Applied Mathematics and Mechanics > 2001 > 22 > 1 > 53-62

*Hamilton Principle was used to derive the general governing equations of nonlinear dynamic stability for laminated cylindrical shells in which, factors of nonlinear large deflection, transverse shear and longitudinal inertia force were concluded. Equations were solved by variational method. Analysis reveals that under the action of dynamic load, laminated cylindrical shells will fall into a state of parametric resonance and enter into the dynamic unstable region that causes dynamic instability of shells. Laminated shells of three typical composites were computed*...

Applied Mathematics and Mechanics > 2001 > 22 > 1 > 105-117

*The non-linear constitutive model suggested by the authors and the Alonso's elasto-plasticity model of unsaturated soil modified by the authors are introduced into the consolidation theory of unsaturated soil proposed by CHEN Zheng-han, and the non-linear and the elasto-plasticity consolidation models of unsaturated soil are obtained. Programs related to the two consolidation models are designed, and a*...

Applied Mathematics and Mechanics > 2001 > 22 > 1 > 1-9

Applied Mathematics and Mechanics > 2001 > 22 > 1 > 89-95

*It is pointed out that crystals are discrete but not continuous materials. Hence the rotation*

**R***in decomposition*

*=*

**F**

**RU***and spin*

**W***in*

**.FF**^{−1}

*are not correct. Errors will arise in plastic deformation rate if it is directly expressed with amounts of velocity of slips in glide systems such as*$$\dot \gamma \nu \otimes n$$ . The geometrical figure of crystal lattices does not change after...

Applied Mathematics and Mechanics > 2001 > 22 > 1 > 35-52

Applied Mathematics and Mechanics > 2001 > 22 > 1 > 118-125

*Similar to the method of continuum mechanics, the variation of the price of index futures is viewed to be continuous and regular. According to the characteristic of index futures, a basic equation of price of index futures was established. It is a differential equation, its solution shows that the relation between time and price forms a logarithmic circle. If the time is thought of as the probability of its corresponding price, then such a relation is perfectly coincided with the main assumption of the famous formula of option pricing, based on statistical theory, established by Black and Scholes, winner of*...

Applied Mathematics and Mechanics > 2001 > 22 > 1 > 79-88

Applied Mathematics and Mechanics > 2001 > 22 > 1 > 10-16

Applied Mathematics and Mechanics > 2001 > 22 > 1 > 17-24

*A method based on newly presented state space formulations is developed for analyzing the bending, vibration and stability of laminated transversely isotropic rectangular plates with simply supported edges. By introducing two displacement functions and two stress functions, two independent state equations were constructed based on the three-dimensional elasticity equations for transverse isotropy. The original differential equations are thus decoupled with the order reduced that will facilitate obtaining solutions of various problems. For the simply supported rectangular plate, two relations between the state variables at the top and bottom surfaces were established. In particular, for the free vibration*...

Applied Mathematics and Mechanics > 2001 > 22 > 1 > 25-34

Applied Mathematics and Mechanics > 2001 > 22 > 1 > 96-104

Applied Mathematics and Mechanics > 2001 > 22 > 1 > 63-78

Applied Mathematics and Mechanics > 2001 > 22 > 2 > 127-134

Applied Mathematics and Mechanics > 2001 > 22 > 2 > 144-153

Applied Mathematics and Mechanics > 2001 > 22 > 2 > 237-260

*Based on new analysis modes and new definitions with relative mathematization and simplification or strengthening forms for concepts of generalized systems, panderivatives, pansymmetry, panbox principle, pansystems relativity, etc., the framework and related principles of pansystems methodology and pansystems relativity are developed. Related contents include*:

*pansystems with relatively universal mathematizing forms*...

Applied Mathematics and Mechanics > 2001 > 22 > 2 > 160-172

Applied Mathematics and Mechanics > 2001 > 22 > 2 > 220-228

Applied Mathematics and Mechanics > 2001 > 22 > 2 > 154-159

Applied Mathematics and Mechanics > 2001 > 22 > 2 > 180-189

Applied Mathematics and Mechanics > 2001 > 22 > 2 > 210-219