--- jupytext: text_representation: extension: .md format_name: myst format_version: 0.13 jupytext_version: 1.16.2 kernelspec: display_name: Python 3 language: python name: python3 --- ```{margin} ::::::{versionadded} v2026.2.0 After workshop 2 Solutions workshop 2 and additional assignments in text and downloads :::::: ::::::{versionadded} v2026.1.0 After workshop 1 Solutions workshop 1 in text and downloads :::::: ::::::{attention} This page shows a preview of the `matrixmethod` package. Please fork and clone the practice assignments to work on it locally from [GitHub](https://github.com/CIEM5000-2026/practice-assignments) After each workshop, the solution will be added to this preview and to the [GitHub-repository](https://github.com/CIEM5000-2026/practice-assignments) :::::: ``` # `constrainer.py` ```{custom_download_link} constrainer.py :text: ".py" :replace_default: "False" ``` ```{custom_download_link} ./matrixmethod_solution/constrainer.py :text: ".py solution workshop 1, 2 and additonal assignments" :replace_default: "False" ``` ```{custom_download_link} https://github.com/CIEM5000-2025/practice-assignments :text: "All files practice assignments" :replace_default: "False" ``` ```{custom_download_link} https://github.com/CIEM5000-2025/practice-assignments/tree/solution_workshop_1 :text: "All files practice assignments with solutions workshop 1" :replace_default: "False" ``` ```{custom_download_link} https://github.com/CIEM5000-2025/practice-assignments/tree/solution_workshop_2 :text: "All files practice assignments with solutions workshop 1" :replace_default: "False" ``` ```{custom_download_link} https://github.com/CIEM5000-2025/practice-assignments/tree/solution_additional_exercises :text: "All files practice assignments with solutions additional exercises" ``` ```{code-cell} ipython3 import numpy as np ``` ```{code-cell} ipython3 class Constrainer: """ A class that represents a constrainer for fixing degrees of freedom in a structural analysis. Attributes: cons_dofs (list): A list of constrained degrees of freedom. cons_vals (list): A list of corresponding constraint values. Methods: fix_dof: Fixes a degree of freedom at a specific value. fix_node: Fixes all degrees of freedom of a node. full_disp: Combines the displacements of free and constrained degrees of freedom. constrain: Applies the constraints to the stiffness matrix and load vector. support_reactions: Calculates the support reactions based on the constrained displacements. """ def __init__(self): """ Initializes a new instance of the Constrainer class. Attributes: cons_dofs (list): A list of constrained degrees of freedom. cons_vals (list): A list of corresponding constraint values. """ self.cons_dofs = [] self.cons_vals = [] def fix_dof (self, node, dof, value = 0): """ Fixes a degree of freedom at a specific value. Args: node (Node): The node object. dof (int): The index of the degree of freedom to fix. value (float, optional): The value to fix the degree of freedom at. Defaults to 0. """ self.cons_dofs.append(node.dofs[dof]) assert value == 0, "Only zero values are supported for now." self.cons_vals.append(value) def fix_node (self, node): """ Fixes all degrees of freedom of a node. Args: node (Node): The node object. """ for dof in [0,1,2]: self.fix_dof (node, dof) def full_disp (self,u_free): """ Combines the displacements of free and constrained degrees of freedom. Args: u_free (numpy.ndarray): The displacements of the free degrees of freedom. Returns: numpy.ndarray: The combined displacements of all degrees of freedom. """ u_full = np.zeros(len(self.free_dofs) + len(self.cons_dofs)) u_full[self.free_dofs] = u_free u_full[self.cons_dofs] = self.cons_vals return u_full def constrain (self, k, f): """ Applies the constraints to the stiffness matrix and load vector. Args: k (numpy.ndarray): The stiffness matrix. f (numpy.ndarray): The load vector. Returns: tuple: A tuple containing the stiffness matrix corresponding to free dofs and the corresponding load vector. """ self.free_dofs = [i for i in range(len(f)) if i not in self.cons_dofs] Kff #= k[np.ix_(YOUR CODE HERE)] Ff # YOUR CODE HERE return Kff, Ff ``` +++ (exercise3_1_py)= ```{solution-start} exercise3.1 :class: dropdown ``` ```{code-cell} ipython3 self.free_dofs = [i for i in range(len(f)) if i not in self.cons_dofs] Kff = k[np.ix_(self.free_dofs,self.free_dofs)] Ff = f[self.free_dofs] return Kff, Ff ``` ```{solution-end} ``` +++ (2_exercise3_1_py_1)= ```{solution-start} 2_exercise3.1 :class: dropdown ``` ```{code-cell} ipython3 self.free_dofs = [i for i in range(len(f)) if i not in self.cons_dofs] Kff = k[np.ix_(self.free_dofs,self.free_dofs)] Kfc = k[np.ix_(self.free_dofs,self.cons_dofs)] Ff = f[self.free_dofs] return Kff, Ff - np.matmul(Kfc,self.cons_vals) ``` ```{solution-end} ``` +++ ```{code-cell} ipython3 def support_reactions (self,k,u_free,f): """ Calculates the support reactions based on the constrained displacements. Args: k (numpy.ndarray): The stiffness matrix. u_free (numpy.ndarray): The displacements of the free degrees of freedom. f (numpy.ndarray): The load vector. Returns: numpy.ndarray: The support reactions. """ #YOUR CODE HERE return #YOUR CODE HERE ``` +++ (2_exercise3_1_py_2)= ```{solution-start} 2_exercise3.1 :class: dropdown ``` ```{code-cell} ipython3 Kcf = k[np.ix_(self.cons_dofs,self.free_dofs)] Kcc = k[np.ix_(self.cons_dofs,self.cons_dofs)] return np.matmul(Kcf,u_free) + np.matmul(Kcc,self.cons_vals) - f[self.cons_dofs] ``` ```{solution-end} ``` +++ ```{code-cell} ipython3 def __str__(self): """ Returns a string representation of the Constrainer object. Returns: str: A string representation of the Constrainer object. """ return f"This constrainer has constrained the degrees of freedom: {self.cons_dofs} with corresponding constrained values: {self.cons_vals})" ```