MITC Study Notes is a local derivation-oriented note set on MITC shell elements. It starts with the motivation for MITC shell elements, then works through shell kinematics, finite element virtual work, Green-Lagrange strain expansion, constitutive matrix transformation, and nonlinear Newmark-beta time integration.
The local source is a converted Markdown/image extraction: two Markdown files and 107 extracted images under .raw/MITC공부/.
Coverage Map
Section
Topic
1
MITC shell element motivation: continuum-degenerated shell behavior and transverse shear locking
2
Shell kinematics: reference/current configurations, director vectors, nodal displacement and rotation variables
3
FE formulation: virtual work, deformation gradient, Green-Lagrange strain, second Piola-Kirchhoff stress, residual and tangent terms
4
Constitutive matrix: plane-stress shell material matrix and coordinate transformation to natural coordinates
MITC shell elements are presented as shell elements derived from a three-dimensional continuum description rather than from a specialized shell theory.
The practical reason for MITC is transverse shear locking control in thin shell analysis.
The kinematic derivation separates nodal translations from director-vector updates, which later feed the incremental displacement field.
The FE formulation uses Green-Lagrange strain and second Piola-Kirchhoff stress, then separates constant, linear, and nonlinear strain terms for tangent construction.
The dynamic section combines Newton-Raphson iteration with Newmark-beta kinematics to obtain an effective equation for displacement increments.
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