3.1.3.2.2. SLS

The SLS (Solid-Like Shell) element is an advanced shell element formulation that combines the computational efficiency of shell elements with the generality of solid elements. It is particularly well-suited for modeling laminated composite structures, layered materials, and sandwich panels where through-thickness behavior is important.

The element uses a solid-like kinematic description with displacement degrees of freedom (u, v, w) and can model multiple layers with different material properties and fiber orientations. It employs static condensation to eliminate internal degrees of freedom, maintaining computational efficiency while capturing complex through-thickness effects.

3.1.3.2.2.1. Overview

Element type: SLS

The element implements:

• Multi-layer capability: Supports layered structures with different materials, thicknesses, and fiber orientations per layer

• Displacement-only formulation: Uses only displacement DOFs (u, v, w) without rotational degrees of freedom

• Static condensation: Internal degrees of freedom are condensed out to improve computational efficiency

• Transverse shear deformation: Accounts for through-thickness shear effects

• Geometric nonlinearity: Can handle moderate geometric nonlinearity

• Composite materials: Fully compatible with anisotropic and transversely isotropic material models

The element is ideal for modeling:

• Laminated composite plates and shells

• Sandwich structures with face sheets and core

• Multi-material layered systems

• Structures requiring accurate through-thickness stress predictions

3.1.3.2.2.2. Parameters

3.1.3.2.2.2.1. Mandatory Parameters

Parameter	Description
type	Must be set to "SLS"
material	Material block defining constitutive behavior. For single-layer elements, specify one material. For multi-layer laminates, use MultiMaterial type. Common material types: "Isotropic": For isotropic materials (parameters: E, nu, rho) "TransverseIsotropic": For unidirectional composites (parameters: E1, E2, nu12, G12, rho) "Orthotropic": For fully orthotropic materials (parameters: E1, E2, E3, nu12, nu13, nu23, G12, G13, G23, rho) "MultiMaterial": For laminates with different materials per layer

3.1.3.2.2.2.2. Optional Parameters

Parameter	Description
theta	Fiber orientation angle in degrees for single-layer elements with anisotropic materials. Specifies the angle between the fiber direction and the element local x-axis. Default is 0.0 if not specified.
layers	List of layer identifiers for multi-layer laminates. Each layer must be defined as a separate block containing: thickness: Layer thickness theta: Fiber orientation angle for this layer (in degrees) material: Material name (when using MultiMaterial type) Example layer definition structure: layers = ["layer1", "layer2", "layer3"]; layer1 = { thickness = 0.5; theta = 0.0; material = "mat1"; };

3.1.3.2.2.3. Examples

3.1.3.2.2.3.1. Example 1: Single-Layer Isotropic Shell

A simple single-layer shell element with isotropic material:

SLSElem =
{
  type = "SLS";

  material =
  {
    type = "Isotropic";
    E    = 1.e6;
    nu   = 0.0;
    rho  = 1.11e3;
  };
};

This configuration is used in: examples/elements/sls/sls_cantilever01.pro

3.1.3.2.2.3.2. Example 2: Unidirectional Composite with Fiber Orientation

A single-layer composite with fibers oriented at an angle:

SLSElem =
{
  type = "SLS";

  material =
  {
    type = "TransverseIsotropic";

    E1   = 1.e6;
    E2   = 5.e5;
    nu12 = 0.25;
    G12  = 4.e5;
    rho  = 1.1e3;
  };

  theta = 45.0;     // Fiber angle in degrees
};

3.1.3.2.2.3.3. Example 3: Multi-Layer Laminate

A three-layer composite laminate with different fiber orientations:

SLSElem0 =
{
  type = "SLS";

  material =
  {
    type = "TransverseIsotropic";

    E1   = 1.e6;
    E2   = 5.e5;
    nu12 = 0.25;
    G12  = 4.e5;
    rho  = 1.1e3;
  };

  theta = 0.0;     // 0-degree layer
};

SLSElem1 =
{
  type = "SLS";

  material =
  {
    type = "TransverseIsotropic";

    E1   = 1.e6;
    E2   = 5.e5;
    nu12 = 0.25;
    G12  = 4.e5;
    rho  = 1.2e3;
  };

  theta = 90.0;    // 90-degree layer
};

SLSElem2 =
{
  type = "SLS";

  material =
  {
    type = "TransverseIsotropic";

    E1   = 1.e6;
    E2   = 5.e5;
    nu12 = 0.25;
    G12  = 4.e5;
    rho  = 1.3e3;
  };

  theta = 0.0;     // 0-degree layer
};

This configuration (0/90/0 laminate) is used in: examples/elements/sls/sls_cantilever02.pro

3.1.3.2.2.4. Additional Examples

The SLS element is demonstrated in several examples in the examples/elements/sls/ directory:

• sls_cantilever01.pro: Basic single-layer cantilever

• sls_cantilever02.pro: Multi-layer laminate configuration

• sls_cantilever03.pro: Advanced layered structure

• sls_cantilever04.pro: Complex laminate example

• sls_cantilever_dyn.pro: Dynamic analysis with SLS elements

3.1.3.2.2.5. Special Features

Static Condensation

The SLS element uses static condensation to eliminate internal degrees of freedom, making it computationally efficient while maintaining accuracy for through-thickness behavior.

Through-Thickness Integration

Multiple integration points through the thickness of each layer provide accurate stress distributions and allow for nonlinear material behavior variation across the thickness.

Composite Modeling

Particularly well-suited for modeling composite laminates where each layer can have different material properties, fiber orientations, and thicknesses.

• materials - Material models for composites

• Plate - Alternative plate element formulation

• smallstraincontinuum - Solid continuum elements

• tutorial1 - Introduction to PyFEM input files