Engineering domain: Structure Design

## Task Description

In this task, you are required to perform a topology optimization to design an optimal cantilever beam structure that minimizes the compliance (maximizes stiffness) under a given volume constraint. The beam is fixed on the left edge and subjected to a downward load at the bottom right corner. The design domain is discretized into a uniform rectangular grid, and material is distributed in this domain to achieve the best structural performance.

## Input Parameters

### Material properties
young = 1
poisson = 0.3

#### Constraints
Emin = 1e-9
volfrac = 0.4
move = 1

#### Mesh dimensions
nelx = 10
nely = 10

## Task
Use the input parameters to set up a topology optimization problem for a cantilever beam. Your task is to:

- Simulate the optimization process.

- Ensure that the design adheres to the specified volume fraction.

- Output the final material distribution, y_hat, and report the minimal compliance value, named C_y_hat, obtained after convergence.

- y_hat must be a matrix where each element ranges from 0 to 1 inclusively.