A theoretical model for impact protection of flexible polymer material

The relationship between the protective performance of flexible polymer material and material parameters(elasticmodulus,viscosity coefficient)is explored,an impact collision motion equation between two bodies is establishedfrom the viscoelastic material constitutive,and the relationship between the kinematic response and the materialparameters is obtained.Based on the Kelvin constitutive model,a theoretical model for impact between the pro-tective body and the protected body is established,then the dynamic response is obtained.The feasibility of themodel was verified by drop hammer experiment,and the material parameters(elastic modulus,viscosity coeffi-cient)were obtained by formula.The model is discretized and the relationship between local impact response andmaterial parameters is analyzed.The discussion results on the relationship between the impact response and theprotective material performance indicate that adjusting the elastic modulus,viscosity coefficient,and thicknessof the protective material can effectively improve protective effect.

Bending the Foundation Beam on Elastic Base by Two Reaction Coefficient of Winkler’s Subgrade

A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.

Response models of weakly consolidated soft rock roadway under different interior pressures considering dilatancy effect

Surrounding rocks of weakly consolidated soft rock roadway show obvious strain softening and dilatancy effects after excavation. A damage coefficient concerning modulus attenuation was defined. Response models of stress and displacement of surrounding rock of soft rock roadway and analytical expressions to calculate plastic zones under different interior pressures and non-uniform original rock stresses were derived based on damage theories and a triple linear elastic-plastic strain softening model. Influence laws of dilatancy gradient on damage development, distributions of stresses and displacement in plastic region were analyzed. Interior pressure conditions to develop plastic region under different origin rock stresses were established and their influences on plastic region distribution were also discussed. The results show that the order of maximum principle stress is exchanged between ~0 and trr with the increase of interior pressure P0, which causes distributions of plastic zone and stress shift. Dilatancy effect which has great influences on the damage propagation and displacements in plastic region has little effect on the size of plastic region and stress responses. The conclusions provide a theoretical basis for a reasonable evaluation of stability and effective supporting of weakly consolidated soft rock roadway.

Size-and temperature-dependent Young's modulus and size-dependent thermal expansion coefficient of nanowires

Nanowires(NWs) exhibit size-dependent mechanical properties due to the high surface/volume ratio, in which temperature also plays an important role. The surface eigenstress model is further developed here to quantitatively predict the size-dependent mechanical properties of NWs and results in analytic formulas. Molecular dynamics(MD) simulations are conducted to study the size-dependent mechanical of [100], [110] and [111] Ni and Si nanowires within the temperature range of 100–400 K and the MD results verify perfectly the newly developed surface eigenstress model.

Optimization of uncertain acoustic metamaterial with Helmholtz resonators based on interval model

In summary,the interval uncertainty is introduced to the acoustic metamaterial with Helmholtz resonators.And then,new descriptions(the conservative approximation,the unsafe approximation and the approximation precision)on uncertainties of physical properties of this interval acoustic metamaterial are defined.Lastly,an optimization model for this interval acoustic metamaterial is proposed.The organization of this paper is listed as follows.The acoustic transmission line method(ATLM)for an acoustic metamaterial with Helmholtz resonators is described in Section 2.In Section3,uncertain analysis of the interval acoustic metamaterial is presented.In Section 4,optimization model of the interval acoustic metamaterial is proposed.The discussion on optimization results is shown in Section 5.In section 6,some conclusions are given.