3.1.3.2.1. Plate

The plate element is an implementation of the Kirchhoff-Love finite element as presented in Chapter 3 of the book XX. The element can be used to model flat structures in the x-y plane as 3, 4, 6 and 8 node elements with 5 degrees of freedom per node. Three translation degrees of freedom (u , v and w) which describe the displacements in the x , y and z direction, respectively, and 2 rotational degrees of freedom (rx and ry) that represent the rotations around the x and y axis, respectively.

3.1.3.2.1.1. Parameters

3.1.3.2.1.1.1. Mandatory Parameters

Parameter	Description
`type`	Must be set to `"Plate"`
`material`	Single-material block defining constitutive behavior (e.g., `E`, `nu`, `rho`) for isotropic plates.
`thickness`	Plate thickness for single-material configurations.

3.1.3.2.1.1.2. Optional Parameters

Parameter

Description

materials

List of material names for multilayer laminates.

layers

List of layer identifiers. Each layer must define:

material — reference to a material name (for materials lists)
theta — fiber orientation angle in degrees
thickness — layer thickness

3.1.3.2.1.1.2.1. Example: Isotropic material

The plate element can be used to model a thin-walled structure, made of a single, isotropic material. In the following example, a plate with a thickness of 1.2 mm is considered, which is made of aluminium. The Young’s modulus is equal to \(E=72\) GPa, the Poisson ratio \(\nu=0.3\) and \(\rho=2780\) kg/m3.

The block in the input file that describes this plate is given below. Please not that all dimensions are in mm, kg and Pa.:

PlateElem =
{
  type = "Plate";

  material =
  {
    E    = 72e9;
    nu   = 0.3;
    rho  = 2780.;
  };

  thickness = 0.0012;
};

This is the end.

3.1.3.2.1.1.2.2. Additional Examples

The Plate element is used in multiple example input files:

examples/elements/plate/plate_cantilever01.pro
examples/elements/plate/plate_cantilever02.pro
examples/plate/platetest.pro
examples/plate/platetest2.pro
examples/plate/plate_test_02.pro
examples/plate/plate_test_03.pro
examples/plate/plate_test_05.pro
examples/plate/plate_test_06.pro
examples/plate/plate_test_07.pro
examples/plate/platedyn.pro
examples/plate/platedynSS.pro

3.1.3.2.1.1.2.3. Example: Layered composite

Alternatively, the element can be used to model flat, composite structures. In the following example, a composite consisting of 5 layers is modeled, with the following stacking sequence:

\[\lbrack 0_w , 0 , 90 , 0 , 0_w\rbrack\]

where \(0_w\) is a woven layer thickness 0.22 mm with the following properties: \(E_1=10\) GPa, \(E_2=10\) GPa, \(\nu_{12}=0.25\) and \(G_{12}=45\) GPa. The three centre layers are made of a UD composite with thickness 0.22 mm and properties: \(E_1=10\) GPa, \(E_2=10\) GPa, \(\nu_{12}=0.25\) and \(G_{12}=45\) GPa.

These properties are given in the input file in the following way:

PlateElem =
{
  type = "Plate";

  materials = [ "Woven" , "UD" ];

  layers = ["W" , "C0" , "C90" , "C0" , "W" ];

  Woven =
  {
    E1   = 1.e6;
    E2   = 0.5e5;
    nu12 = 0.3;
    G12  = 1.0e6;
    rho  = 1.0e3;
  };

  UD =
  {
    E1   = 1.e6;
    E2   = 0.5e5;
    nu12 = 0.3;
    G12  = 1.0e6;
    rho  = 1.0e3;
  };

  W =
  {
    material  = "Woven";
    theta     = 0.;
    thickness = 0.05;
  };

  C0 =
  {
    material  = "UD";
    theta     = 0.;
    thickness = 0.05;
  };

  C90 =
  {
    material  = "UD";
    theta     = 90.;
    thickness = 0.05;
  };
};

This is the end.