nCMCMA (non-Continuous-Material Cube Modal Analysis)

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📦 Downloads (v0.1.0-alpha)

Pre-compiled binary releases for Linux and Windows are available under GitHub Releases.

Platform	File	Quick Run Command
Linux (All Distros)	ncmcma-v0.1.0-alpha-linux-x64.tar.gz	Copy this whole command in terminal: cd Downloads && tar -xzvf ncmcma-v0.1.0-alpha-linux-x64.tar.gz && ./ncmcma-v0.1.0-alpha-linux-x64/run.sh
Windows (10/11 x64)	ncmcma-v0.1.0-alpha-win64.zip	Extract .zip and run ncmcma.exe

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nCMCMA is designed for the structural modal analysis and dynamic response simulation of 3D non-continuous material cube structures (mass-spring lattice models).

The software constructs global Mass ($M$), Stiffness ($K$), and Rayleigh Damping ($C$) matrices for a discretized $N \times N \times N$ mass-spring system with 6 degrees of freedom (DOF) per mass element. It solves state-space eigenvalue problems and computes frequency-domain receptance matrices and dynamic displacements ($q = \alpha(\omega) \cdot Q$) with OpenMP multi-threading acceleration.

Calculates natural frequency with iteration, older verison were calculating all natural frequencies but this takes too much time and really high RAM usage and segmentation faults (for massNum = 16 -> ~19GB, but now it takes a few houndred MB). This iteration results may looks like natural freq. values too close but this is not a mistake. This model is not fem(finite element method). The lattice structure causes this. Still if you increase massNum, time increase exponentally but ram usage is npt that much because of the iteration algotihm.

The simulation may not show the springs but I draw an example.

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Structural Sample Model for a $2 \times 2 \times 2$ mass lattice

Below is an illustration of a $2 \times 2 \times 2$ mass lattice (massNum{2}) configuration with interconnected spring-damper elements:

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Memory WARNING

If you increase lattice size (massNum) more than 16, probably your memory won't be enough and you will take a crash after half an hour. So, consider that this simulatin is only for experimental. Performance and resource usage is not worked on well area. There is a reposity I am working on currently, it will be better about that, actually it will be a finished fem engine, so this project is made for test-education purpose.

Features

• 3D Mass-Spring Lattice Generation: Flexible setup for $N \times N \times N$ discrete cube structures with 6 DOFs per node (3 translational + 3 rotational).
• State-Space Formulation: Conversion of system matrices into $2N \times 2N$ state-space representation for precise eigenvalue and natural frequency extraction.
• Rayleigh Damping Integration: Material-specific Rayleigh damping matrix calculation ($\mathbf{C} = \alpha \mathbf{M} + \beta \mathbf{K}$).
• Receptance Matrix Computation: Computes frequency-dependent transfer function matrices $\boldsymbol{\alpha}(\omega) = (\mathbf{K} - \omega^2 \mathbf{M} + i \omega \mathbf{C})^{-1}$ using Eigen's FullPivLU solver.
• Dynamic Load Response ($q = \alpha(\omega) Q$): Calculates complex spatial displacements and magnitudes across all DOFs under applied dynamic forces.
• Multi-Threaded Parallel Execution: Utilizes OpenMP and Eigen parallelization, automatically scaled to half of system hardware threads for optimal performance and thermal efficiency.
• Visualization: with imgui and opengl, colored spheres according to their displacement. Shows element has higher displacement red (doesn't animates strings for better look, only sphere mass-elements)

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Screenshot From GUI

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Project Structur

nCMCMA/
├── CMakeLists.txt              # Build configuration with C++23, Eigen3 & OpenMP
├── main.cpp                    # Application entry point & parallel analysis runner
├── 2_2_2_cubeSample.png        # Sample lattice model diagram
└── src/
    ├── engine
    │   ├── simEngine.cpp           # parallel analysis runner
    │   └── simEngine.h
    ├── gui
    │   ├── gui.cpp                 # visualize the results
    │   └── gui.h
    ├── matrixOperations/
    │   ├── stdEigenValueSolver.h
    │   └── stdEigenValueSolver.cpp # Eigen-based eigenvalue solver & frequency extractor
    └── modalAnalysis/
        ├── massMatrix.h
        ├── massMatrix.cpp          # Mass matrix generation (6 DOF / node)
        ├── stiffMatrix.h
        └── stiffMatrix.cpp         # Stiffness matrix assembly

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Prerequisites

• C++ Compiler: C++23 support (e.g., g++ 12+ or clang 14+)
• Build System: CMake 3.22 or higher
• Libraries:
  • Eigen 3.3+ (Linear algebra library)
  • OpenMP (Multi-threading support)

Installing Dependencies

There are 4 dependencies: openGL for animation, imGui for gui, Eigen for matrix computations, openMP for multithreading.

Ubuntu/Debian

sudo apt update
sudo apt install -y build-essential cmake ninja-build g++-13 libeigen3-dev libglfw3-dev libgl1-mesa-dev libglu1-mesa-dev libomp-dev

Fedora

sudo dnf check-update
sudo dnf install -y @development-tools cmake ninja-build gcc-c++ eigen3-devel glfw-devel mesa-libGL-devel mesa-libGLU-devel libomp-devel glew-devel freeglut-devel
sudo dnf install wayland-devel libwayland-client libwayland-cursor libwayland-egl libxkbcommon-devel
sudo dnf install libXrandr-devel libXinerama-devel libXcursor-devel libXi-devel libXext-devel

warning: I did not check all of them is necessary or not and asked AI and it gave me those, probably most of them is unnecesary. I'm sorry to not checking but fedora feels a bit weird to me about packages.

Arch/CachyOS

sudo pacman -Syu --needed base-devel cmake ninja gcc eigen glfw-x11 mesa openmp

Windows

in PowerShell

git clone https://github.com/microsoft/vcpkg.git
cd vcpkg
.\bootstrap-vcpkg.bat
.\vcpkg integrate install

.\vcpkg install eigen3:x64-windows
.\vcpkg install glfw3:x64-windows
.\vcpkg install glad:x64-windows

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Building & Running

1. Configure and Build

cmake -B build -S .
cmake --build build

for windows

cmake -B build -S . -DCMAKE_TOOLCHAIN_FILE="C:/vcpkg/scripts/buildsystems/vcpkg.cmake"
cmake --build build --config Debug

2. Run Execution

./build/ncmcma

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📊 Mathematical Formulation

1. Governing Equation: $$\mathbf{M} \ddot{\mathbf{x}}(t) + \mathbf{C} \dot{\mathbf{x}}(t) + \mathbf{K} \mathbf{x}(t) = \mathbf{Q}(t)$$

2. Receptance Matrix ( $\boldsymbol{\alpha}(\omega)$ ): $$\boldsymbol{\alpha}(\omega) = \left( \mathbf{K} - \omega^2 \mathbf{M} + i \omega \mathbf{C} \right)^{-1}$$

3. Dynamic Response Calculation ($q$): $$\mathbf{q}(\omega) = \boldsymbol{\alpha}(\omega) \cdot \mathbf{Q}(\omega)$$

Process Flow

$$\begin{matrix} K, M \xrightarrow{\text{Diagonal Transformation}} S = M^{-1/2} K M^{-1/2} \end{matrix}$$

$$\begin{matrix} A = S + I \xrightarrow{\text{LDLT Decomposition}} A = L D L^T \end{matrix}$$

$$\begin{matrix} \text{25 x Iter: } V_k = A^{-1} Q_k \xrightarrow{\text{QR}} Q_{k+1} \end{matrix}$$

$$\begin{matrix} T = Q^T S Q \xrightarrow{\text{Rayleigh-Ritz}} \text{eig}(T) \rightarrow \lambda \end{matrix}$$

$$\begin{matrix} \omega = \sqrt{\lambda} \end{matrix}$$