Static analysis of elastic cable structures under mechanical load using discrete catenary theory

In this paper,the nonlinear mechanical response of elastic cable structures under mechanical load is studied based on the discrete catenary theory.A cable net is discretized into multiple nodes and edges in our numerical approach,which is followed by an analytical formulation of the elastic energy and the associated Hessian matrix to realize the dynamic simulation.A fully implicit framework is proposed based on the discrete differential geometry(DDG)theory.The equilibrium configuration of a target object is derived by adding damping force into the system,known as the dynamic relaxation method.The mechanical response of a single suspended cable is investigated and compared with the analytical solution for cross-validation.A more intricate scenario is further discussed in detail,where a structure consisting of multiple slender cables is connected through joints.Utilizing the robustness and efficiency of our discrete numerical framework,a systematic parameter sweep is performed to quantify the force displacement relationships of nets with the different number of cables and different directions of fibers.Finally,an empirical scaling law is provided to account for the rigidity of elastic cable net in terms of its geometric properties,material characteristics,component numbers,and cable orientations.Our results would provide new insight in revealing the connections between flexible structures and tensegrity structures,and could motivate innovative designs in both mechanical and civil engineered equipment.

Dark energy versus modified gravity: Impacts on measuring neutrino mass

In this paper,we make a comparison for the impacts of smooth dynamical dark energy,modified gravity,and interacting dark energy on the cosmological constraints on the total mass of active neutrinos.For definiteness,we consider theΛCDM model,the w CDM model,the f(R)model,and two typical interacting vacuum energy models,i.e.,the IΛCDM1 model with Q=βHρc and the IΛCDM2 model with Q=βHρΛ.In the cosmological fits,we use the Planck 2015 temperature and polarization data,in combination with other low-redshift observations including the baryon acoustic oscillations,the type Ia supernovae,the Hubble constant measurement,and the large-scale structure observations,such as the weak lensing as well as the redshift-space distortions.Besides,the Planck lensing measurement is also employed in this work.We find that,the w CDM model favors a higher upper limit on the neutrino mass compared to theΛCDM model,while the upper limit in the f(R)model is similar with that in theΛCDM model.For the interacting vacuum energy models,the IΛCDM1 model favors a higher upper limit on neutrino mass,while the IΛCDM2 model favors an identical neutrino mass with the case ofΛCDM.