From Deformation Theory to Interactive Visualization: Development of an Application for Engineering Education

This paper connects a critical review of the publicly documented SpaceX CRS-7 failure sequence with a progressive computational study of structural deformation. The first part examines the qualification of the composite overwrapped pressure vessel support hardware, the structural load path, and the limitations of the publicly available evidence. Fatigue, elastic stability, and thermoelastic relations are discussed as general structural-mechanics screening tools and are not presented as demonstrated causes of the accident.

The second part develops a sequence of MATLAB-based numerical applications for the analysis and visualisation of infinitesimal and finite deformations. The investigation begins with the deformation of a two-dimensional square, continues with image warping and the transformation of a three-dimensional cube, and subsequently considers position-dependent mappings, shared-node connectivity, and an illustrative static-loading case. Particular attention is given to the deformation gradient, the Green–Lagrange strain tensor, polar decomposition, finite rotations, and the conditions required for a physically admissible transformation.

The study culminates in DeForm, an interactive MATLAB application that applies prescribed deformation and rotation parameters to a three-dimensional representation of the letter “M” and compares linearised and nonlinear affine transformations in real time.

The proposed framework is intended primarily as an educational and visualisation tool for introductory structural-mechanics and continuum-kinematics courses. The associated MATLAB source code and supplementary animations are available through the project repository.