Vehicle-cpp/hkpc/software/sympy/physics/continuum_mechanics/truss.py

"""
This module can be used to solve problems related
to 2D Trusses.
"""

from cmath import inf
from sympy.core.add import Add
from sympy.core.mul import Mul
from sympy.core.symbol import Symbol
from sympy.core.sympify import sympify
from sympy import Matrix, pi
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.matrices.dense import zeros
from sympy import sin, cos



class Truss:
    """
    A Truss is an assembly of members such as beams,
    connected by nodes, that create a rigid structure.
    In engineering, a truss is a structure that
    consists of two-force members only.

    Trusses are extremely important in engineering applications
    and can be seen in numerous real-world applications like bridges.

    Examples
    ========

    There is a Truss consisting of four nodes and five
    members connecting the nodes. A force P acts
    downward on the node D and there also exist pinned
    and roller joints on the nodes A and B respectively.

    .. image:: truss_example.png

    >>> from sympy.physics.continuum_mechanics.truss import Truss
    >>> t = Truss()
    >>> t.add_node("node_1", 0, 0)
    >>> t.add_node("node_2", 6, 0)
    >>> t.add_node("node_3", 2, 2)
    >>> t.add_node("node_4", 2, 0)
    >>> t.add_member("member_1", "node_1", "node_4")
    >>> t.add_member("member_2", "node_2", "node_4")
    >>> t.add_member("member_3", "node_1", "node_3")
    >>> t.add_member("member_4", "node_2", "node_3")
    >>> t.add_member("member_5", "node_3", "node_4")
    >>> t.apply_load("node_4", magnitude=10, direction=270)
    >>> t.apply_support("node_1", type="fixed")
    >>> t.apply_support("node_2", type="roller")
    """

    def __init__(self):
        """
        Initializes the class
        """
        self._nodes = []
        self._members = {}
        self._loads = {}
        self._supports = {}
        self._node_labels = []
        self._node_positions = []
        self._node_position_x = []
        self._node_position_y = []
        self._nodes_occupied = {}
        self._reaction_loads = {}
        self._internal_forces = {}
        self._node_coordinates = {}

    @property
    def nodes(self):
        """
        Returns the nodes of the truss along with their positions.
        """
        return self._nodes

    @property
    def node_labels(self):
        """
        Returns the node labels of the truss.
        """
        return self._node_labels

    @property
    def node_positions(self):
        """
        Returns the positions of the nodes of the truss.
        """
        return self._node_positions

    @property
    def members(self):
        """
        Returns the members of the truss along with the start and end points.
        """
        return self._members

    @property
    def member_labels(self):
        """
        Returns the members of the truss along with the start and end points.
        """
        return self._member_labels

    @property
    def supports(self):
        """
        Returns the nodes with provided supports along with the kind of support provided i.e.
        pinned or roller.
        """
        return self._supports

    @property
    def loads(self):
        """
        Returns the loads acting on the truss.
        """
        return self._loads

    @property
    def reaction_loads(self):
        """
        Returns the reaction forces for all supports which are all initialized to 0.
        """
        return self._reaction_loads

    @property
    def internal_forces(self):
        """
        Returns the internal forces for all members which are all initialized to 0.
        """
        return self._internal_forces

    def add_node(self, label, x, y):
        """
        This method adds a node to the truss along with its name/label and its location.

        Parameters
        ==========
        label:  String or a Symbol
            The label for a node. It is the only way to identify a particular node.

        x: Sympifyable
            The x-coordinate of the position of the node.

        y: Sympifyable
            The y-coordinate of the position of the node.

        Examples
        ========

        >>> from sympy.physics.continuum_mechanics.truss import Truss
        >>> t = Truss()
        >>> t.add_node('A', 0, 0)
        >>> t.nodes
        [('A', 0, 0)]
        >>> t.add_node('B', 3, 0)
        >>> t.nodes
        [('A', 0, 0), ('B', 3, 0)]
        """
        x = sympify(x)
        y = sympify(y)

        if label in self._node_labels:
            raise ValueError("Node needs to have a unique label")

        elif x in self._node_position_x and y in self._node_position_y and self._node_position_x.index(x)==self._node_position_y.index(y):
            raise ValueError("A node already exists at the given position")

        else :
            self._nodes.append((label, x, y))
            self._node_labels.append(label)
            self._node_positions.append((x, y))
            self._node_position_x.append(x)
            self._node_position_y.append(y)
            self._node_coordinates[label] = [x, y]

    def remove_node(self, label):
        """
        This method removes a node from the truss.

        Parameters
        ==========
        label:  String or Symbol
            The label of the node to be removed.

        Examples
        ========

        >>> from sympy.physics.continuum_mechanics.truss import Truss
        >>> t = Truss()
        >>> t.add_node('A', 0, 0)
        >>> t.nodes
        [('A', 0, 0)]
        >>> t.add_node('B', 3, 0)
        >>> t.nodes
        [('A', 0, 0), ('B', 3, 0)]
        >>> t.remove_node('A')
        >>> t.nodes
        [('B', 3, 0)]
        """
        for i in range(len(self.nodes)):
            if self._node_labels[i] == label:
                x = self._node_position_x[i]
                y = self._node_position_y[i]

        if label not in self._node_labels:
            raise ValueError("No such node exists in the truss")

        else:
            members_duplicate = self._members.copy()
            for member in members_duplicate:
                if label == self._members[member][0] or label == self._members[member][1]:
                    raise ValueError("The node given has members already attached to it")
            self._nodes.remove((label, x, y))
            self._node_labels.remove(label)
            self._node_positions.remove((x, y))
            self._node_position_x.remove(x)
            self._node_position_y.remove(y)
            if label in list(self._loads):
                self._loads.pop(label)
            if label in list(self._supports):
                self._supports.pop(label)
            self._node_coordinates.pop(label)

    def add_member(self, label, start, end):
        """
        This method adds a member between any two nodes in the given truss.

        Parameters
        ==========
        label: String or Symbol
            The label for a member. It is the only way to identify a particular member.

        start: String or Symbol
            The label of the starting point/node of the member.

        end: String or Symbol
            The label of the ending point/node of the member.

        Examples
        ========

        >>> from sympy.physics.continuum_mechanics.truss import Truss
        >>> t = Truss()
        >>> t.add_node('A', 0, 0)
        >>> t.add_node('B', 3, 0)
        >>> t.add_node('C', 2, 2)
        >>> t.add_member('AB', 'A', 'B')
        >>> t.members
        {'AB': ['A', 'B']}
        """

        if start not in self._node_labels or end not in self._node_labels or start==end:
            raise ValueError("The start and end points of the member must be unique nodes")

        elif label in list(self._members):
            raise ValueError("A member with the same label already exists for the truss")

        elif self._nodes_occupied.get((start, end)):
            raise ValueError("A member already exists between the two nodes")

        else:
            self._members[label] = [start, end]
            self._nodes_occupied[start, end] = True
            self._nodes_occupied[end, start] = True
            self._internal_forces[label] = 0

    def remove_member(self, label):
        """
        This method removes a member from the given truss.

        Parameters
        ==========
        label: String or Symbol
            The label for the member to be removed.

        Examples
        ========

        >>> from sympy.physics.continuum_mechanics.truss import Truss
        >>> t = Truss()
        >>> t.add_node('A', 0, 0)
        >>> t.add_node('B', 3, 0)
        >>> t.add_node('C', 2, 2)
        >>> t.add_member('AB', 'A', 'B')
        >>> t.add_member('AC', 'A', 'C')
        >>> t.add_member('BC', 'B', 'C')
        >>> t.members
        {'AB': ['A', 'B'], 'AC': ['A', 'C'], 'BC': ['B', 'C']}
        >>> t.remove_member('AC')
        >>> t.members
        {'AB': ['A', 'B'], 'BC': ['B', 'C']}
        """
        if label not in list(self._members):
            raise ValueError("No such member exists in the Truss")

        else:
            self._nodes_occupied.pop((self._members[label][0], self._members[label][1]))
            self._nodes_occupied.pop((self._members[label][1], self._members[label][0]))
            self._members.pop(label)
            self._internal_forces.pop(label)

    def change_node_label(self, label, new_label):
        """
        This method changes the label of a node.

        Parameters
        ==========
        label: String or Symbol
            The label of the node for which the label has
            to be changed.

        new_label: String or Symbol
            The new label of the node.

        Examples
        ========

        >>> from sympy.physics.continuum_mechanics.truss import Truss
        >>> t = Truss()
        >>> t.add_node('A', 0, 0)
        >>> t.add_node('B', 3, 0)
        >>> t.nodes
        [('A', 0, 0), ('B', 3, 0)]
        >>> t.change_node_label('A', 'C')
        >>> t.nodes
        [('C', 0, 0), ('B', 3, 0)]
        """
        if label not in self._node_labels:
            raise ValueError("No such node exists for the Truss")
        elif new_label in self._node_labels:
            raise ValueError("A node with the given label already exists")
        else:
            for node in self._nodes:
                if node[0] == label:
                    self._nodes[self._nodes.index((label, node[1], node[2]))] = (new_label, node[1], node[2])
                    self._node_labels[self._node_labels.index(node[0])] = new_label
                    self._node_coordinates[new_label] = self._node_coordinates[label]
                    self._node_coordinates.pop(label)
                    if node[0] in list(self._supports):
                        self._supports[new_label] = self._supports[node[0]]
                        self._supports.pop(node[0])
                    if new_label in list(self._supports):
                        if self._supports[new_label] == 'pinned':
                            if 'R_'+str(label)+'_x' in list(self._reaction_loads) and 'R_'+str(label)+'_y' in list(self._reaction_loads):
                                self._reaction_loads['R_'+str(new_label)+'_x'] = self._reaction_loads['R_'+str(label)+'_x']
                                self._reaction_loads['R_'+str(new_label)+'_y'] = self._reaction_loads['R_'+str(label)+'_y']
                                self._reaction_loads.pop('R_'+str(label)+'_x')
                                self._reaction_loads.pop('R_'+str(label)+'_y')
                            self._loads[new_label] = self._loads[label]
                            for load in self._loads[new_label]:
                                if load[1] == 90:
                                    load[0] -= Symbol('R_'+str(label)+'_y')
                                    if load[0] == 0:
                                        self._loads[label].remove(load)
                                    break
                            for load in self._loads[new_label]:
                                if load[1] == 0:
                                    load[0] -= Symbol('R_'+str(label)+'_x')
                                    if load[0] == 0:
                                        self._loads[label].remove(load)
                                    break
                            self.apply_load(new_label, Symbol('R_'+str(new_label)+'_x'), 0)
                            self.apply_load(new_label, Symbol('R_'+str(new_label)+'_y'), 90)
                            self._loads.pop(label)
                        elif self._supports[new_label] == 'roller':
                            self._loads[new_label] = self._loads[label]
                            for load in self._loads[label]:
                                if load[1] == 90:
                                    load[0] -= Symbol('R_'+str(label)+'_y')
                                    if load[0] == 0:
                                        self._loads[label].remove(load)
                                    break
                            self.apply_load(new_label, Symbol('R_'+str(new_label)+'_y'), 90)
                            self._loads.pop(label)
                    else:
                        if label in list(self._loads):
                            self._loads[new_label] = self._loads[label]
                            self._loads.pop(label)
                    for member in list(self._members):
                        if self._members[member][0] == node[0]:
                            self._members[member][0] = new_label
                            self._nodes_occupied[(new_label, self._members[member][1])] = True
                            self._nodes_occupied[(self._members[member][1], new_label)] = True
                            self._nodes_occupied.pop((label, self._members[member][1]))
                            self._nodes_occupied.pop((self._members[member][1], label))
                        elif self._members[member][1] == node[0]:
                            self._members[member][1] = new_label
                            self._nodes_occupied[(self._members[member][0], new_label)] = True
                            self._nodes_occupied[(new_label, self._members[member][0])] = True
                            self._nodes_occupied.pop((self._members[member][0], label))
                            self._nodes_occupied.pop((label, self._members[member][0]))

    def change_member_label(self, label, new_label):
        """
        This method changes the label of a member.

        Parameters
        ==========
        label: String or Symbol
            The label of the member for which the label has
            to be changed.

        new_label: String or Symbol
            The new label of the member.

        Examples
        ========

        >>> from sympy.physics.continuum_mechanics.truss import Truss
        >>> t = Truss()
        >>> t.add_node('A', 0, 0)
        >>> t.add_node('B', 3, 0)
        >>> t.nodes
        [('A', 0, 0), ('B', 3, 0)]
        >>> t.change_node_label('A', 'C')
        >>> t.nodes
        [('C', 0, 0), ('B', 3, 0)]
        >>> t.add_member('BC', 'B', 'C')
        >>> t.members
        {'BC': ['B', 'C']}
        >>> t.change_member_label('BC', 'BC_new')
        >>> t.members
        {'BC_new': ['B', 'C']}
        """
        if label not in list(self._members):
            raise ValueError("No such member exists for the Truss")

        else:
            members_duplicate = list(self._members).copy()
            for member in members_duplicate:
                if member == label:
                    self._members[new_label] = [self._members[member][0], self._members[member][1]]
                    self._members.pop(label)
                    self._internal_forces[new_label] = self._internal_forces[label]
                    self._internal_forces.pop(label)

    def apply_load(self, location, magnitude, direction):
        """
        This method applies an external load at a particular node

        Parameters
        ==========
        location: String or Symbol
            Label of the Node at which load is applied.

        magnitude: Sympifyable
            Magnitude of the load applied. It must always be positive and any changes in
            the direction of the load are not reflected here.

        direction: Sympifyable
            The angle, in degrees, that the load vector makes with the horizontal
            in the counter-clockwise direction. It takes the values 0 to 360,
            inclusive.

        Examples
        ========

        >>> from sympy.physics.continuum_mechanics.truss import Truss
        >>> from sympy import symbols
        >>> t = Truss()
        >>> t.add_node('A', 0, 0)
        >>> t.add_node('B', 3, 0)
        >>> P = symbols('P')
        >>> t.apply_load('A', P, 90)
        >>> t.apply_load('A', P/2, 45)
        >>> t.apply_load('A', P/4, 90)
        >>> t.loads
        {'A': [[P, 90], [P/2, 45], [P/4, 90]]}
        """
        magnitude = sympify(magnitude)
        direction = sympify(direction)

        if location not in self.node_labels:
            raise ValueError("Load must be applied at a known node")

        else:
            if location in list(self._loads):
                self._loads[location].append([magnitude, direction])
            else:
                self._loads[location] = [[magnitude, direction]]

    def remove_load(self, location, magnitude, direction):
        """
        This method removes an already
        present external load at a particular node

        Parameters
        ==========
        location: String or Symbol
            Label of the Node at which load is applied and is to be removed.

        magnitude: Sympifyable
            Magnitude of the load applied.

        direction: Sympifyable
            The angle, in degrees, that the load vector makes with the horizontal
            in the counter-clockwise direction. It takes the values 0 to 360,
            inclusive.

        Examples
        ========

        >>> from sympy.physics.continuum_mechanics.truss import Truss
        >>> from sympy import symbols
        >>> t = Truss()
        >>> t.add_node('A', 0, 0)
        >>> t.add_node('B', 3, 0)
        >>> P = symbols('P')
        >>> t.apply_load('A', P, 90)
        >>> t.apply_load('A', P/2, 45)
        >>> t.apply_load('A', P/4, 90)
        >>> t.loads
        {'A': [[P, 90], [P/2, 45], [P/4, 90]]}
        >>> t.remove_load('A', P/4, 90)
        >>> t.loads
        {'A': [[P, 90], [P/2, 45]]}
        """
        magnitude = sympify(magnitude)
        direction = sympify(direction)

        if location not in self.node_labels:
            raise ValueError("Load must be removed from a known node")

        else:
            if [magnitude, direction] not in self._loads[location]:
                raise ValueError("No load of this magnitude and direction has been applied at this node")
            else:
                self._loads[location].remove([magnitude, direction])
        if self._loads[location] == []:
            self._loads.pop(location)

    def apply_support(self, location, type):
        """
        This method adds a pinned or roller support at a particular node

        Parameters
        ==========

        location: String or Symbol
            Label of the Node at which support is added.

        type: String
            Type of the support being provided at the node.

        Examples
        ========

        >>> from sympy.physics.continuum_mechanics.truss import Truss
        >>> t = Truss()
        >>> t.add_node('A', 0, 0)
        >>> t.add_node('B', 3, 0)
        >>> t.apply_support('A', 'pinned')
        >>> t.supports
        {'A': 'pinned'}
        """
        if location not in self._node_labels:
            raise ValueError("Support must be added on a known node")

        else:
            if location not in list(self._supports):
                if type == 'pinned':
                    self.apply_load(location, Symbol('R_'+str(location)+'_x'), 0)
                    self.apply_load(location, Symbol('R_'+str(location)+'_y'), 90)
                elif type == 'roller':
                    self.apply_load(location, Symbol('R_'+str(location)+'_y'), 90)
            elif self._supports[location] == 'pinned':
                if type == 'roller':
                    self.remove_load(location, Symbol('R_'+str(location)+'_x'), 0)
            elif self._supports[location] == 'roller':
                if type == 'pinned':
                    self.apply_load(location, Symbol('R_'+str(location)+'_x'), 0)
            self._supports[location] = type

    def remove_support(self, location):
        """
        This method removes support from a particular node

        Parameters
        ==========

        location: String or Symbol
            Label of the Node at which support is to be removed.

        Examples
        ========

        >>> from sympy.physics.continuum_mechanics.truss import Truss
        >>> t = Truss()
        >>> t.add_node('A', 0, 0)
        >>> t.add_node('B', 3, 0)
        >>> t.apply_support('A', 'pinned')
        >>> t.supports
        {'A': 'pinned'}
        >>> t.remove_support('A')
        >>> t.supports
        {}
        """
        if location not in self._node_labels:
            raise ValueError("No such node exists in the Truss")

        elif location not in list(self._supports):
            raise ValueError("No support has been added to the given node")

        else:
            if self._supports[location] == 'pinned':
                self.remove_load(location, Symbol('R_'+str(location)+'_x'), 0)
                self.remove_load(location, Symbol('R_'+str(location)+'_y'), 90)
            elif self._supports[location] == 'roller':
                self.remove_load(location, Symbol('R_'+str(location)+'_y'), 90)
            self._supports.pop(location)

    def solve(self):
        """
        This method solves for all reaction forces of all supports and all internal forces
        of all the members in the truss, provided the Truss is solvable.

        A Truss is solvable if the following condition is met,

        2n >= r + m

        Where n is the number of nodes, r is the number of reaction forces, where each pinned
        support has 2 reaction forces and each roller has 1, and m is the number of members.

        The given condition is derived from the fact that a system of equations is solvable
        only when the number of variables is lesser than or equal to the number of equations.
        Equilibrium Equations in x and y directions give two equations per node giving 2n number
        equations. However, the truss needs to be stable as well and may be unstable if 2n > r + m.
        The number of variables is simply the sum of the number of reaction forces and member
        forces.

        .. note::
           The sign convention for the internal forces present in a member revolves around whether each
           force is compressive or tensile. While forming equations for each node, internal force due
           to a member on the node is assumed to be away from the node i.e. each force is assumed to
           be compressive by default. Hence, a positive value for an internal force implies the
           presence of compressive force in the member and a negative value implies a tensile force.

        Examples
        ========

        >>> from sympy.physics.continuum_mechanics.truss import Truss
        >>> t = Truss()
        >>> t.add_node("node_1", 0, 0)
        >>> t.add_node("node_2", 6, 0)
        >>> t.add_node("node_3", 2, 2)
        >>> t.add_node("node_4", 2, 0)
        >>> t.add_member("member_1", "node_1", "node_4")
        >>> t.add_member("member_2", "node_2", "node_4")
        >>> t.add_member("member_3", "node_1", "node_3")
        >>> t.add_member("member_4", "node_2", "node_3")
        >>> t.add_member("member_5", "node_3", "node_4")
        >>> t.apply_load("node_4", magnitude=10, direction=270)
        >>> t.apply_support("node_1", type="pinned")
        >>> t.apply_support("node_2", type="roller")
        >>> t.solve()
        >>> t.reaction_loads
        {'R_node_1_x': 0, 'R_node_1_y': 20/3, 'R_node_2_y': 10/3}
        >>> t.internal_forces
        {'member_1': 20/3, 'member_2': 20/3, 'member_3': -20*sqrt(2)/3, 'member_4': -10*sqrt(5)/3, 'member_5': 10}
        """
        count_reaction_loads = 0
        for node in self._nodes:
            if node[0] in list(self._supports):
                if self._supports[node[0]]=='pinned':
                    count_reaction_loads += 2
                elif self._supports[node[0]]=='roller':
                    count_reaction_loads += 1
        if 2*len(self._nodes) != len(self._members) + count_reaction_loads:
            raise ValueError("The given truss cannot be solved")
        coefficients_matrix = [[0 for i in range(2*len(self._nodes))] for j in range(2*len(self._nodes))]
        load_matrix = zeros(2*len(self.nodes), 1)
        load_matrix_row = 0
        for node in self._nodes:
            if node[0] in list(self._loads):
                for load in self._loads[node[0]]:
                    if load[0]!=Symbol('R_'+str(node[0])+'_x') and load[0]!=Symbol('R_'+str(node[0])+'_y'):
                        load_matrix[load_matrix_row] -= load[0]*cos(pi*load[1]/180)
                        load_matrix[load_matrix_row + 1] -= load[0]*sin(pi*load[1]/180)
            load_matrix_row += 2
        cols = 0
        row = 0
        for node in self._nodes:
            if node[0] in list(self._supports):
                if self._supports[node[0]]=='pinned':
                    coefficients_matrix[row][cols] += 1
                    coefficients_matrix[row+1][cols+1] += 1
                    cols += 2
                elif self._supports[node[0]]=='roller':
                    coefficients_matrix[row+1][cols] += 1
                    cols += 1
            row += 2
        for member in list(self._members):
            start = self._members[member][0]
            end = self._members[member][1]
            length = sqrt((self._node_coordinates[start][0]-self._node_coordinates[end][0])**2 + (self._node_coordinates[start][1]-self._node_coordinates[end][1])**2)
            start_index = self._node_labels.index(start)
            end_index = self._node_labels.index(end)
            horizontal_component_start = (self._node_coordinates[end][0]-self._node_coordinates[start][0])/length
            vertical_component_start = (self._node_coordinates[end][1]-self._node_coordinates[start][1])/length
            horizontal_component_end = (self._node_coordinates[start][0]-self._node_coordinates[end][0])/length
            vertical_component_end = (self._node_coordinates[start][1]-self._node_coordinates[end][1])/length
            coefficients_matrix[start_index*2][cols] += horizontal_component_start
            coefficients_matrix[start_index*2+1][cols] += vertical_component_start
            coefficients_matrix[end_index*2][cols] += horizontal_component_end
            coefficients_matrix[end_index*2+1][cols] += vertical_component_end
            cols += 1
        forces_matrix = (Matrix(coefficients_matrix)**-1)*load_matrix
        self._reaction_loads = {}
        i = 0
        min_load = inf
        for node in self._nodes:
            if node[0] in list(self._loads):
                for load in self._loads[node[0]]:
                    if type(load[0]) not in [Symbol, Mul, Add]:
                        min_load = min(min_load, load[0])
        for j in range(len(forces_matrix)):
            if type(forces_matrix[j]) not in [Symbol, Mul, Add]:
                if abs(forces_matrix[j]/min_load) <1E-10:
                    forces_matrix[j] = 0
        for node in self._nodes:
            if node[0] in list(self._supports):
                if self._supports[node[0]]=='pinned':
                    self._reaction_loads['R_'+str(node[0])+'_x'] = forces_matrix[i]
                    self._reaction_loads['R_'+str(node[0])+'_y'] = forces_matrix[i+1]
                    i += 2
                elif self._supports[node[0]]=='roller':
                    self._reaction_loads['R_'+str(node[0])+'_y'] = forces_matrix[i]
                    i += 1
        for member in list(self._members):
            self._internal_forces[member] = forces_matrix[i]
            i += 1
        return