In this project, structural topology optimization is performed on 3D structures. An Iso-geometric code based on NURBS volume is generated for parametric details. The advantage of NURBS over Lagrangian basis function is NURBS can correctly interpret geometry as it doesn't approximate it which allows us to build complex optimized structure which have less compliance. Unlike FEM, application of boundary condition in IGA for higher order basis function is quite difficult and special strategy like least square method have to be used. Only first order NURBS basis functions are used in IGTO due to difficulty in visualization of the structure for higher order basis. The optimization problem is solved using OC (optimality criterion) and MMA (method of moving asymptotes). From the analysing results, we can conclude that for iso-geometric topology optimization (IGTO) MMA is better suited as it is gradient based method and converges rapidly compared to OC. With OC, the solution may never reach optimal solution as it uctuates about the constrain. Performance of OC can be optimized by using additional filters (Heavy side filter). The in uence of parameters like penalization factor and minimum radius on topology optimization is performed and discreteness of volume in the structure is calculated. To get checker-board free pattern,p greater then 3.5. The penalization factor depends on Young's modulus and Poissons ratio.

The following steps should be performed to run the program and test cases. All the files are written in python.

All python files have to be placed in same folder and working directory has to be same to run the python program. Python version 3.7.4 can be used to run this python code.

1. A file name main program.py is the starting point of the IGTO program. command: python main program.py (a) Required python external libraries like 'numpy', 'matplotlib', 'pyvista', 'pyEVTK','pytest' are checked and installed.

0- Time analysis (log files are generated)

Enter - For normal execution without any log files.

3.Then the inputs have to be given or press enter to run default values.

l h w nx ny nz load volume_fra penal rmin E v density BC_op Ft_op verbose

8 5 1 35 25 3 -100 0.4 3 1.5 150000 0.3 7850 0 1 1

Length(l) : 8

Height(h) : 5

Width(w) : 1

nx(no of elements along x) : 35

ny(no of elements along y) : 25

nz(no of elements along z) : 3

load : -100

volume_fraction : 0.4

penal : 3

rmin : 1.5

E(Youngs modulus) : 150000

v(poisson ratio) : 0.3

density : 7850

BC_op : 0

Ft_op : 1

verbose : 1

Options :

0- Cantilever beam with load along the bottom edge of the free end.

1- Simple supported with point load at bottom center.

2- Cantilever beam with point load at bottom of the free end.

3- Cantilever beam with point load at the free end (2d case loading at y=height and x=length).

4- Cantilever beam with two forces at top and bottom of the free end .

5- Cantilever beam with point load at the center of the free end.

6- Simple supported with load at top center.

Options :

0-OC (optimality criterion)

1-MMA (method of moving asymptotes)

Options :

0-Will not print plots using pyvista only VTK file is generated.

1- Plots are generated and stored in results folder.

We used pytest to perform unit, functional and patch testing. All test files are the python files which contain respective test cases. All files should be placed in the same folder and the working directory has to be same, so that test cases can run.

2. test geometry.py : Test cases on shape function and assembly

3. test element routine.py : Test cases on integration scheme and sanity checks on other element.

4. test optimization.py : Test cases on optimizer function OC(optimality cri- terion) and MMA(method of moving asymptotes)

5. test rigid body motion.py : Test cases to validate global stiffness matrix and boundary conditions by performing rigid body translation and rotation.

6. test patch.py : Test cases on constant stress patch test and comparing an- alytical solution with numerical for lower and higher order shape functions.

To run all the test cases, copy all test files in same folder and enter PYTEST command on the terminal.