Study Of Plastic Tensile Instability And Buckling In Hyperbolic Thin Metal Shells With Circular Base And Application In Engineering

Peripherally clamped thin shallow hyperbolic metal shells under internal or external pressure are widely used to protect equipments from overpressure or to meet some particular needs in technical processes as quick opening devices. Tension-loaded shell deforms from original flat sheet up to bulge rupturing. Geometrically, the problem has the character of large displacement and finite strain. Compression-loaded shell is formed after unloading from pre-bulged shell, the pressure is on the convex of shell, and elastic-plastic buckling occurs when it works. It is more important that the thin metal shells have to be ruptured or collapsed in a rigorous set pressure range, just the contrary of usual engineering design with safety margin. It is quite difficult to get analytic solution since nonlinear coupling exists between geometry and constitution. Only some empirical formulae are currently used to calculate the rupture pressure in engineering application. In this paper, the problem is investigated by analytic method, finite element method, and experimental research.(1) An improved method is put forward for the biaxial tensile test of sheet metals. The influence of spring-back on the curvature radius at the pole is reckoned in. Errors derived from the approximate hypotheses of spherical profile and uniform thinning can be avoided. Then the relationship between true stress and true strain in the full deformation range of sheet metals can thus be built up.(2) Based on large deformation geometrical relations, a mathematical model described with differential algebraic equations is presented for axisymmetric thin hyperbolic metal shell with variable thickness under internal pressure, which remedies the low precision in solving large deformation problems based on Gleyzal's geometrical relations expanded with Taylor's formula. Numerical solutions are carried out using Klopfenstein-Shampine numerical differentiation formulae. The distribution of stresses, strains, and displacements of metal shell at specific times can be obtained.A method is put forward to calculate the tensile instability load of axisymmetric thin metal shell. The instability load is the possible ultimate pressure in the common satisfaction of the constitutive relations, geometrical equations, and static equilibrium relations. Relatively large errors of existing simplified geometrical relations are studied, and then a high precision formula for design calculation is established.Based on condition of biaxial tension instability, this paper reveals that strain-hardening exponent of sheet metals has no influence on the theoretic tensile instability pressure, and the instability pressure is positively proportional to the strength coefficient of materials.(3) Tension-loaded radial slotted thin sheets, radial slotted thin shells, and radial notched thin shells have the characteristics of large deformation, variable curvature, and variable thickness. Comprehensive study has been carried out for the sheets or shells by finite element analysis and experiments.Influence of up-holder corner on the mechanical behavior of bulging shell is closely related to the similarity criterion ru/s0. The influence is partitioned into four regions by three demarcation points of ru/s0= 0.52, 1.50, and 2.00. Orderly, there are regions of full effect, unstable region, near-stable region, and region of no effect. The results can be applied in engineering application.Specific relationships between plastic tensile instability pressure and main structural parameters such as deflections, bridge-lengths, and thickness in notches are established. Then the design formulae of tensile instability pressure for these tension-loaded structures are represented.(4) The non-linear buckling behavior of axisymmetric thin shells and thin-notched shells, subjected to pressure on convex, is investigated with the method of wave-distributed imperfection. The geometric imperfection is a linear combination of the first buckling mode.At first, the influence of negative-curvature zone on the buckling behavior o...