Nonlinear dynamic analysis of inflating axisymmetric membranes subjected to contact constraints

Conference · Wed Jun 04 04:00:00 EDT 1975

OSTI ID:7366969

Hallquist, J O; Feng, W W

The exact governing equations of motion for finite deformations of hyperelastic membranes subjected to a contact constraint are derived from Hamilton's principle. The constraint condition is eliminated by introducing a slack coordinate as a new variable. An approximate solution to the resulting equations is sought by means of the Rayleigh-Ritz procedure in which a series of geometrically admissible continuous shape functions multiplied by unknown time dependent coefficients are assumed to define the deformed configurations. A set of nonlinear simultaneous differential equations are obtained and are solved by Newmark's method with Newton-Raphson iterations. As a consequence of the contact surface the inertial terms in the governing equations are nonlinear functions of the current displacements, velocities, and accelerations. A numerical example is presented in dimensionless form to demonstrate the effectiveness of the procedure.

• Research Organization: California Univ., Livermore (USA). Lawrence Livermore Lab.
• OSTI ID: 7366969
• Report Number(s): UCRL-77095; CONF-760404-2
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420200* -- Engineering-- Facilities
Equipment
& Techniques
DEFORMATION
DIFFERENTIAL EQUATIONS
EQUATIONS
MEMBRANES
NONLINEAR PROBLEMS
NUMERICAL SOLUTION