Large deflections of shallow conical membrane

Large deflections of a shallow elastic conical membrane fixed at the outer edge and loaded by either uniform or hydrostatic pressure are investigated. The overning equations were solved by the method of matched asymptotic expansions and by a finite difference method. Agreement between the two methods was excellent for the small values of the perturbation parameter

One-dimensional wave propagation in particulate suspensions

One-dimensional small-amplitude wave motion in a two-phase system consisting of an inviscid gas and a cloud of suspended particles is analyzed using a continuum theory of suspensions. Laplace transform methods are used to obtain several approximate solutions. Properties of acoustic wave motion in particulate suspensions are inferred from these solutions

Similarity Rules for Scaling Solar Sail Systems

Future science missions will require solar sails on the order of 200 square meters (or larger). However, ground demonstrations and flight demonstrations must be conducted at significantly smaller sizes, due to limitations of ground-based facilities and cost and availability of flight opportunities. For this reason, the ability to understand the process of scalability, as it applies to solar sail system models and test data, is crucial to the advancement of this technology. This paper will approach the problem of scaling in solar sail models by developing a set of scaling laws or similarity criteria that will provide constraints in the sail design process. These scaling laws establish functional relationships between design parameters of a prototype and model sail that are created at different geometric sizes. This work is applied to a specific solar sail configuration and results in three (four) similarity criteria for static (dynamic) sail models. Further, it is demonstrated that even in the context of unique sail material requirements and gravitational load of earth-bound experiments, it is possible to develop appropriate scaled sail experiments. In the longer term, these scaling laws can be used in the design of scaled experimental tests for solar sails and in analyzing the results from such tests

A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams

This paper presents a nonlocal sinusoidal shear deformation beam theory for the bending, buckling, and vibration of nanobeams. The present model is capable of capturing both small scale effect and transverse shear deformation effects of nanobeams, and does not require shear correction factors. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion as well as the boundary conditions of the beam are derived using Hamilton’s principle. Analytical solutions for the deflection, buckling load, and natural frequency are presented for a simply supported beam, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory. The comparison firmly establishes that the present beam theory can accurately predict the bending, buckling, and vibration responses of short nanobeams where the small scale and transverse shear deformation effects are significant

Lie symmetry analysis and numerical solutions for thermo-solutal chemicallyreacting radiative micropolar flow from an inclined porous surface

Steady, laminar, incompressible thermo-solutal natural convection flow of micropolar fluid from an inclined perforated surface with convective boundary conditions is studied. Thermal radiative flux and chemical reaction effects are included to represent phenomena encountered in high-temperature materials synthesis operations. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. A Lie scaling group transformation is implemented to derive a self-similar form of the partial differential conservation equations. The resulting coupled nonlinear boundary value problem is solved with Runge-Kutta fourth order numerical quadrature (shooting technique). Validation of solutions with an optimized Adomian decomposition method algorithm is included. Verification of the accuracy of shooting is also conducted as a particular case of non-reactive micropolar flow from a vertical permeable surface. The evolution of velocity, angular velocity (micro-rotation component), temperature and concentration are examined for a variety of parameters including coupling number, plate inclination angle, suction/injection parameter, radiation-conduction parameter, Biot number and reaction parameter. Numerical results for steady state skin friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are tabulated and discussed. Interesting features of the hydrodynamic, heat and mass transfer characteristics are examined

Convergence analysis of Laplacian-based gradient elasticity in an isogeometric framework

A convergence study is presented for a form of gradient elasticity where the enrichment is through the Laplacian of the strain, so that a fourth-order partial differential equation results. Isogeometric finite element analysis is used to accommodate the higher continuity required by the inclusion of strain gradients. A convergence analysis is carried out for the original system of a fourth-order partial differential equation. Both global refinement, using NURBS, and local refinement, using T-splines, have been applied. Theoretical convergence rates are recovered, except for a polynomial order of two, when the convergence rate is suboptimal, a result which also has been found for the (fourth-order) Cahn-Hilliard equation. The convergence analyses have been repeated for the case that an operator split is applied so that a set of two (one-way) coupled partial differential equations results. Differences occur with the results obtained for the original fourth-order equation, which is caused by the boundary conditions, which is the first time this effect has been substantiated

Influence of variable viscosity and thermal conductivity, hydrodynamic and thermal slips on magnetohydrodynamic micropolar flow: a numerical study

Thermophysical and wall slip effects arise in many areas of nuclear technology. Motivated by such applications, in this article the collective influence ofvariable viscosity, thermal conductivity, velocity and thermal slipseffects on a steady two-dimensional magnetohydrodynamic microplar fluid over a stretching sheet are analyzednumerically. The governing nonlinear partial differential equations have been converted into a system of non-linear ordinary differential equations using suitable coordinate transformations. The numerical solutions of the problem are expressed in the form of non-dimensional velocityand temperature profiles and discussed from their graphical representations. Nachtsheim-Swigert shooting iteration technique together withthesixth order Runge-Kutta integration scheme has been applied for the numerical solution.A comparison with the existing results has been done and an excellent agreement is found.Further validation with adomian decomposition method is included for the general model. Interesting features in the heat and momentum characteristics are explored. It is found that greater thermal slip and thermal conductivity elevate thermal boundary layer thickness. Increasing Prandtl number enhances Nusselt number at the wall but reduces wall couple stress (micro-rotation gradient). Temperatures are enhanced with both magnetic field and viscosity parameter. Increasing momentum (hydrodynamic) slip is found to accelerate the flow and elevate temperatures