r3.07.06 Eccentricity treatment for plate elements DKT, DST,, DKQ, dsq, and q4g

Summary:

[R3.07.03] plate elements are intended for the calculations of three-dimensional thin structures. The middle layer of these structures does not always coincide with the draft plane or mesh plane. The concept of eccentricity of the middle sheet with respect to the drawing plane is therefore introduced. It can be used for elements taking into account transverse shear, or without this hypothesis.

Table of Contents

• 1. Introduction
• 2. Formulation
  • 2.1. Geometry
  • 2.2. Cinematics
  • 2.3. Law of behavior
• 3. Principle of virtual work
  • 3.1. Deformation work
  • 3.2. Work of forces and external couples
  • 3.3. Principle of virtual work and balance equations
• 4. Numerical discretization of variational formulation based on the principle of virtual work
  • 4.1. Introduction
  • 4.2. Discretization of the displacement field
  • 4.3. Taking into account transverse distortion
  • 4.4. Elementary stiffness matrix
  • 4.5. Elementary mass matrix
• 5. Implementation and post-treatments
  • 5.1. Application of efforts and couples
  • 5.2. Application of boundary conditions while traveling
  • 5.3. Post-treatments
• 6. Static and modal validation
  • 6.1. Initial validation
  • 6.2. Test case SSLS111: eccentricity for simple plates
  • 6.3. Test case SSLS112: eccentricity for composite plates
• 7. Conclusion
• 8. Bibliographical references
• 9. Description of document versions