MITC4 Shell Element
This API is a package designed for nonlinear finite element simulations with the MITC4 shell element. The nonlinear analysis is based on the Updated Lagrangian Configuration (co-rotational approach). The package includes the computation of the Stiffness Matrix, the Geometrical (or Initial Stress) Stiffness Matrix, and the Internal Force Vector.
Developed in C++ for Linux and Windows operating systems.
Get to know the MITC4 Shell Element Class
Description of the element's Class; its constructor and Public Methods that can be used.
Mesh Convergence & Aircraft Wing Results
Hemispherical Shell Benchmark: A rigorous convergence test with mesh refinement for testing element's accuracy with warped shell element configurations under large rotations analysis.
Designed to push the limits of element performance under extreme warping, transverse shear, and bending loads.
The MITC4 shell element API achieves fast convergence with mesh refinement.
Explore the gallery for an in-depth analysis of the mesh convergence results and post-processing in our GUI.
Click on the gallery below for the MITC4 Shell API convergence results and post-processing on our GUI for the Hemispherical Shell example.
Aircraft Wing linear elastic simulation with the MITC4 shell API
An application example of the MITC4 Shell API is presented through the linear elastic simulation of an aircraft wing. The wing is fixed at the root (fuselage) and subjected to impulse loading at the landing gear attachment point.
This simulation utilized our free C++ linear elastic template, with pre-processing and post-processing performed using our GUI. The results are showcased in the image gallery below.
Constituents of the API
Stiffness Matrix
Stiffness matrix for the MITC4 shell element. Required for linear and nonlinear analysis.
B-Matrix
Shell element with 4 nodes and full in-plane quadrature rule. User-defined number of integration points along the thickness direction of the shell. Reissner-Mindlin formulation with ANS to alleviate transverse shear locking. Ideal for thin shell simulations.
Geometric Stiffness Matrix
Geometric (Initial Stresses) Stiffness matrix for the MITC4 shell element. It is required for nonlinear analysis with implicit time integration scheme, buckling analysis, etc.
Internal Force (available soon)
Internal Force vector for the MITC4 shell element. Critical for nonlinear analysis for both explicit and implicit time integration schemes.
Strain Tensor
Strain tensor at all integration points of the element. The strain tensor can be used for different type of constitutive models.
Axes Rotation at the GPs (available soon)
Rotation of local axes at the Gauss Points. Important for nonlinear co-rotational analysis, e.g. rotation of planar plastic anisotropic axes, rotation of composites ply axes at the GPs.
Compile, Install & Use of the API
// STIFFNESS
//
// loop in the elements
for (iel = 0; iel < melems; ++iel) {
.
.
.
// instance of the API: Calls the Constructor for this element
NonlinearShellMITC4 stif(xyz_in,vnor_in,thick_in,xlocal_in,ylocal_in,zetCoord,zetWeigt,stresses,DMatrix_all);
StiffnessTotal = stif.Calculate_StiffnessMITC4();
}
Extract of the free template distributed with the API for the calculation of the stiffness of the element.
NonlinearShellMITC4 is the Class of the API
stif is one Instance of the Class
Calculate_StiffnessMITC4() is a method of the API's Class to calculate the stiffness matrix of the element
The free template provided with the API leverages OpenMP for multi-threading the element loop, significantly accelerating the computation of the total stiffness matrix.
cmake_minimum_required(VERSION 3.22)
project(Linear_Elastic_ShellMITC4)
set(CMAKE_CXX_STANDARD 20)
#
# Include for the header files
set(INCLUDE_DIRS ".../path to the include folder")
include_directories(${INCLUDE_DIRS})
# Specify the name of the library (API)
set(LIBRARY_NAME libNonlinearShellMITC4.so)
set(MYLIB_LIBRARY_DIR ".../path to the library folder")
# Find OpenMP (crucial if multi-threading OpenMP is to be used)
find_package(OpenMP REQUIRED)
# Create the executable
add_executable(${PROJECT_NAME} main.cpp Nodes.cpp Elements.cpp IO_APIs_Shells.cpp
Utils.cpp FaceLoad.cpp)
# Link against the shared library
target_link_directories(${PROJECT_NAME} PUBLIC ${MYLIB_LIBRARY_DIR})
# Link OpenMP to your executable
target_link_libraries(${PROJECT_NAME} PUBLIC armadillo NonlinearShellMITC4 OpenMP::OpenMP_CXX)
CMakeLists.txt file for the linear elastic free template distributed with the API (Linux)
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