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In this paper separation-induced shock reflection is studied theoretically and experimentally. An analytical model is proposed to establish the connections among upstream conditions, downstream conditions and shock configurations. Furthermore, the minimum entropy production principle is employed to determine the incident shock angles as well as the criterion for the transition from regular reflection to Mach reflection, which agrees well with experimental results. Additionally, a solution path for a reflected shock that fulfills the minimum entropy production principle is found in the overall regular reflection domain, based on which the steadiest shock configuration may be determined according to upstream and downstream conditions.

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In this paper, the well-known Hencky problem—that is, the problem of axisymmetric deformation of a peripherally fixed and initially flat circular membrane subjected to transverse uniformly distributed loads—is re-solved by simultaneously considering the improvement of the out-of-plane and in-plane equilibrium equations. In which, the so-called small rotation angle assumption of the membrane is given up when establishing the out-of-plane equilibrium equation, and the in-plane equilibrium equation is, for the first time, improved by considering the effect of the deflection on the equilibrium between the radial and circumferential stress. Furthermore, the resulting nonlinear differential equation is successfully solved by using the power series method, and a new closed-form solution of the problem is finally presented. The conducted numerical example indicates that the closed-form solution presented here has a higher computational accuracy in comparison with the existing solutions of the well-known Hencky problem, especially when the deflection of the membrane is relatively large.

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