A new approach to applying the finite difference method for solving the shell model problem. By solving the general shell differential equations (Sanders-Koiter equations) with first-order finite-difference approximation only, a finite difference algorithm called shell code has been developed.

To this end, a 1200-line Python program has been built. In the process many versions of shell code were considered, including
1) Two programming languages (Python and R)
2) Three interpolations for approximating gradients (three-point and five-point with two end slopes)
3) Determined and over-determined systems of equations (square and rectangular matrices)
4) Four solvers for the systems of equations

The final version of shell code has the following features; five-point interpolation with zero end slope, rectangular matrix, solver lm.fit.sparse (R). Approximately 80% of the shell code results match the finite element results with a deviation less than 5%. It has been proved that the selected version of shell code can solve shell model problems by solving Sanders-Koiter equations with finite difference method. Many previously assumed important factor for affecting shell code results, like number of nodes and interpolation methods, were actually less significant. However, the most vital difference in results occurred under different computation methods. Maybe under further research of developing mathematic tools, finite difference method could be a more promising and practical method for solving model problems.

A new approach to applying the finite difference method for solving the plate model problem. By decomposing higher-order differential equations in plate theory into several first-order differential equations, a python program was built in an attempt to solve those equations with first-order finite difference approximation. After testing several square plate models with various boundary and load conditions, this program has been proved to work. The major results (displacement, bending moment, and shear force) are generally 10 to 20% smaller than the analytical solutions. The difference can be caused by the grid size but also by a programming error. Compared to the finite element method, this python program has a smaller code size but with less accuracy and more computational time.