Generalized Marguerre-von Kármán Equations for a Nonlinearly Elastic Shallow Shell

Using techniques from asymptotic analysis, we identify equations that generalize the classical Marguerre-von Kármán equations. These more general equations are justified by means of the leading term of a formal asymptotic expansion of the solution to the three-dimensional equations of nonlinear elasticity associated with a specific class of boundary conditions that characterizes "generalized Marguerre-von Kármán shallow shells".

Keywords:

• Nonlinear Elasticity
• Asymptotic Analysis
• Shallow Shell Theory
• Marguerre-von Kármán Equations