Fully Inverse Constitutive Matrix Composite Material
Matrix Inversion Calculator
Inverse of Constitutive Matrix For Composite
The inverse of this matrix allows engineers to determine the strain and curvature responses ϵ0 and k of the material to applied forces and moments N and M, providing insights into how the composite will deform under various loads. This inverse relationship is critical for designing and analyzing the structural behavior of composite materials in advanced applications like aerospace and automotive engineering.
![\[ \begin{Bmatrix} \epsilon_x^0 \\ \epsilon_y^0 \\ \gamma_{xy}^0 \\ k_x \\ k_y \\ k_{xy} \end{Bmatrix} = \begin{bmatrix} A_{11} & A_{12} & A_{16} & B_{11} & B_{12} & B_{16} \\ A_{12} & A_{22} & A_{26} & B_{12} & B_{22} & B_{26} \\ A_{16} & A_{26} & A_{66} & B_{16} & B_{26} & B_{66} \\ B_{11} & B_{12} & B_{16} & D_{11} & D_{12} & D_{16} \\ B_{12} & B_{22} & B_{26} & D_{12} & D_{22} & D_{26} \\ B_{16} & B_{26} & B_{66} & D_{16} & D_{26} & D_{66} \end{bmatrix}^{-1} \begin{Bmatrix} N_x \\ N_y \\ N_{xy} \\ M_x \\ M_y \\ M_{xy} \end{Bmatrix} \]](http://pttensor.com/wp-content/ql-cache/quicklatex.com-335628bb443f5f0205defc5bf53593f9_l3.png "Rendered by QuickLaTeX.com")
Related Module(s): Constitutive matrix,
TensorConnect project 2024 by pttensor.com Author: Caesar Wiratama