INCREMENTAL ANALYSIS OF NONLINEAR STRUCTURAL MECHANICS PROBLEMS WITH APPLICATIONS TO GENERAL SHELL STRUCTURES

The primary theme is the nonlinear behavior of shell structures. A general formulation that can be applied to all structures is derived and then specialized for application to shells through the development of a quadrilateral shell finite element. The formulation is in incremental form and is derived in terms of the material coordinate system. The procedure evolved to solve the nonlinear equilibrium equations allows for the inclusion of all terms as opposed to previous incremental procedures where the equations are linearized. The derivation of the formulation and solution procedure is independent of the finite element method, but it is this method that is used to exercise and apply the formulation. An elementary nonlinear problem is first solved and then more complex problems are studied by using the formulation and solution procedure. The quadrilateral shell element which is introduced uses the exact geometry of the shell surface in the computation of stiffness matrices and loads. A consistent method is used for transforming the element and its properties; this improves element effectiveness for application to branched and reinforced shells. The shell surface geometry is used in the enforcement of the continuity of displacements for satisfying the convergence requirements. The ability of the element to undergo rigid body motion without causing strains is examined by studying the eigenvalues of the stiffness matrix of an element.

• Supplemental Notes:
  • The report is based on a Doctor of Philosophy dissertation submitted to the Catholic University of America.
• Corporate Authors:

  Naval Ship Research and Development Center

  Structures Department
  Bethesda, MD  United States  20034
• Authors:
  • Jones Jr, R F
• Publication Date: 1973-9

Media Info

• Features: References;
• Pagination: 100 p.

Subject/Index Terms

• TRT Terms: Deformation; Finite element method; Shells (Structural forms); Stiffness matrix
• Old TRIS Terms: Shell deformation; Stiffness matrices
• Subject Areas: Marine Transportation; Materials;

Filing Info

• Accession Number: 00051175
• Record Type: Publication
• Source Agency: Naval Ship Research and Development Center
• Report/Paper Numbers: Paper #4142 Final Rpt
• Files: TRIS
• Created Date: Feb 28 1974 12:00AM