caa a22 4500 475840135 CHVBK 20180406123859.0 cr unu---uuuuu 170329e20000201xx s 000 0 eng 10.1023/A:1004709622104 doi (NATIONALLICENCE)springer-10.1023/A:1004709622104 Application of variational principles to the axial extension of a circular cylindical nonlinearly elastic membrane [Elektronische Daten] [J. Haddow, L. Favre, R. Ogden] In this paper stationary potential-energy and complementary-energy principles are formulated for boundary-value problems for compressible or incompressible nonlinearly elastic membranes, and full justification for adoption of the complementary principle is provided. The stationary principles are then extended to extremum principles, which provide upper and lower bounds on the energy functional associated with the solution of a given problem. The principles are then illustrated by their application to the nonlinear problem of the axially symmetric static deformation of an isotropic elastic membrane. In its undeformed natural configuration the membrane has the form of a circular cylindrical surface. The cylinder is subject to a prescribed (tensile) axial force with the ends of the cylinder constrained so that their radii remain constant. The alternative boundary condition in which the axial displacement of the ends is prescribed instead of the axial force is also considered. The extremum principles are applied first without restriction on the form of strain-energy function in order to obtain primitive bounds on the energy of Voigt and Reuss type commonly used in composite-material mechanics. Then, for particular forms of strain-energy function, specific bounds are obtained by selecting suitable trial deformation and stress fields and the bounds are optimized using a numerical procedure (which is readily adapted for other forms of strain-energy function). It is found that these bounds are very close and hence give a good estimate of the actual energy. The associated deformed geometry of the membrane is described together with the resulting principal stresses. Kluwer Academic Publishers, 2000 nonlinear elasticity nationallicence elastic membranes nationallicence variational principles nationallicence Haddow J. Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, V8W 3P6, Victoria, BC, Canada aut Favre L. Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, V8W 3P6, Victoria, BC, Canada aut Ogden R. Department of Mathematics, University of Glasgow, University Gardens, G12 8QW, Glasgow, U.K. aut Journal of Engineering Mathematics Kluwer Academic Publishers 37/1-3(2000-02-01), 65-84 0022-0833 37:1-3<65 2000 37 10665 https://doi.org/10.1023/A:1004709622104 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004709622104 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Haddow J. Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, V8W 3P6, Victoria, BC, Canada aut NATIONALLICENCE 700 1- Favre L. Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, V8W 3P6, Victoria, BC, Canada aut NATIONALLICENCE 700 1- Ogden R. Department of Mathematics, University of Glasgow, University Gardens, G12 8QW, Glasgow, U.K aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Kluwer Academic Publishers 37/1-3(2000-02-01), 65-84 0022-0833 37:1-3<65 2000 37 10665 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer