o *ήcT@s.dZddlmZddlmZGdddZdS)zB This module can be used to solve problems related to 2D Trusses. )Symbol)sympifyc@seZdZdZddZeddZeddZedd Zed d Z ed d Z eddZ eddZ eddZ eddZddZddZddZddZddZd d!Zd"d#Zd$d%Zd&d'Zd(d)Zd*S)+Trussa 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") cCsFg|_i|_i|_i|_g|_g|_g|_g|_i|_i|_ i|_ dS)z' Initializes the class N) _nodes_members_loads _supports _node_labels_node_positions_node_position_x_node_position_y_nodes_occupied_reaction_loads_internal_forcesselfrN/tmp/pip-target-vg8gfxp4/lib/python/sympy/physics/continuum_mechanics/truss.py__init__/s zTruss.__init__cC|jS)zL Returns the nodes of the truss along with their positions. )rrrrrnodes?z Truss.nodescCr)z7 Returns the node labels of the truss. )r rrrr node_labelsFrzTruss.node_labelscCr)zB Returns the positions of the nodes of the truss. )r rrrrnode_positionsMrzTruss.node_positionscCrzW Returns the members of the truss along with the start and end points. )rrrrrmembersTrz Truss.memberscCrr)_member_labelsrrrr member_labels[rzTruss.member_labelscCr)z Returns the nodes with provided supports along with the kind of support provided i.e. pinned or roller. )rrrrrsupportsbszTruss.supportscCr)z8 Returns the loads acting on the truss. )rrrrrloadsjrz Truss.loadscCr)z^ Returns the reaction forces for all supports which are all initialized to 0. )rrrrrreaction_loadsqrzTruss.reaction_loadscCr)z] Returns the internal forces for all members which are all initialized to 0. )rrrrrinternal_forcesxrzTruss.internal_forcescCst|}t|}||jvrtd||jvr+||jvr+|j||j|kr+td|j|||f|j||j||f|j||j|dS)a 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)] z!Node needs to have a unique labelz+A node already exists at the given positionN) rr ValueErrorr r indexrappendr )rlabelxyrrradd_nodes ,  zTruss.add_nodecCs tt|jD]}|j||kr|j|}|j|}q||jvr$td|j}|D]}||j|dks?||j|dkrCtdq+|j |||f|j ||j ||f|j ||j ||t |j vrt|j ||t |jvr|j|dSdS)a% 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)] z No such node exists in the trussrz1The node given has members already attached to itN)rangelenrr r r r"rcopyrremover listrpopr)rr%ir&r'members_duplicatememberrrr remove_nodes,    $    zTruss.remove_nodecCs||jvs||jvs||krtd|t|jvrtd|jt||gr+td||g|j|<d|j||f<d|j||f<d|j|<dS)a 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']} z;The start and end points of the member must be unique nodesz9A member with the same label already exists for the trussz-A member already exists between the two nodesTrN)r r"r.rr gettupler)rr%startendrrr add_memberszTruss.add_membercCs|t|jvr td|jt|j|d|j|dg|jt|j|d|j|dg|j||j|dS)a 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']} z"No such member exists in the Trussrr)N)r.rr"r r/r5r)rr%rrr remove_members (( zTruss.remove_memberc Cs||jvr td||jvrtd|jD]F}|d|kr\||d|df|j|j||d|df<||j|j|d<|dt|jvr\|j|d|j|<|j|d|t|jvr|j|dkrRdt|dt|jvrdt|d t|jvr|jdt|d|jdt|d<|jdt|d |jdt|d <|jdt|d|jdt|d |j ||j |<|j |D](}|dd kr|dt dt|d 8<|ddkr|j | |nq|j |D]+}|ddkr+|dt dt|d8<|ddkr)|j | |nq| |t dt|dd| |t dt|d d |j |nm|j|d kr|j ||j |<|j |D]+}|dd kr|dt dt|d 8<|ddkr|j | |nqg| |t dt|d d |j |n|t|j vr|j ||j |<|j |t|j D]}|j |d|dkr||j |d<d |j||j |df<d |j|j |d|f<|jt||j |dg|jt|j |d|gq|j |d|dkrZ||j |d<d |j|j |d|f<d |j||j |df<|jt|j |d|g|jt||j |dgqqd S)a 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)] z!No such node exists for the Trussz*A node with the given label already existsrr)pinnedR__x_yZrollerTN)r r"rr#r.rr/strrrrr- apply_loadrr r5)rr% new_labelnodeloadr2rrrchange_node_label's   .4((       "zTruss.change_node_labelcCs|t|jvr tdt|j}|D]+}||kr?|j|d|j|dg|j|<|j||j||j|<|j|qdS)aG 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']} z#No such member exists for the Trussrr)N)r.rr"r,r/r)rr%rCr1r2rrrchange_member_labels "  zTruss.change_member_labelcCs\t|}t|}||jvrtd|t|jvr$|j|||gdS||gg|j|<dS)a This method applies an external load at a particular node Parameters ========== location: String or Symbol Label of the Node at which load is applied. magnitude: Sympifyable Magnitude of the load applied. It must always be positive and any changes in the direction of the load are not reflected here. direction: Sympifyable The angle, in degrees, that the load vector makes with the horizontal in the counter-clockwise direction. It takes the values 0 to 360, inclusive. Examples ======== >>> from sympy.physics.continuum_mechanics.truss import Truss >>> from sympy import symbols >>> t = Truss() >>> t.add_node('A', 0, 0) >>> t.add_node('B', 3, 0) >>> P = symbols('P') >>> t.apply_load('A', P, 90) >>> t.apply_load('A', P/2, 45) >>> t.apply_load('A', P/4, 90) >>> t.loads {'A': [[P, 90], [P/2, 45], [P/4, 90]]} z$Load must be applied at a known nodeN)rrr"r.rr$rlocation magnitude directionrrrrBs! zTruss.apply_loadcCsrt|}t|}||jvrtd||g|j|vrtd|j|||g|j|gkr7|j|dSdS)a; This method removes an already present external load at a particular node Parameters ========== location: String or Symbol Label of the Node at which load is applied and is to be removed. magnitude: Sympifyable Magnitude of the load applied. direction: Sympifyable The angle, in degrees, that the load vector makes with the horizontal in the counter-clockwise direction. It takes the values 0 to 360, inclusive. Examples ======== >>> from sympy.physics.continuum_mechanics.truss import Truss >>> from sympy import symbols >>> t = Truss() >>> t.add_node('A', 0, 0) >>> t.add_node('B', 3, 0) >>> P = symbols('P') >>> t.apply_load('A', P, 90) >>> t.apply_load('A', P/2, 45) >>> t.apply_load('A', P/4, 90) >>> t.loads {'A': [[P, 90], [P/2, 45], [P/4, 90]]} >>> t.remove_load('A', P/4, 90) >>> t.loads {'A': [[P, 90], [P/2, 45]]} z&Load must be removed from a known nodezENo load of this magnitude and direction has been applied at this nodeN)rrr"rr-r/rHrrr remove_loads$ zTruss.remove_loadcCs||jvr td|t|jvrG|dkr3||tdt|dd||tdt|ddnI|dkrF||tdt|ddn5|j|dkrb|dkra||tdt|ddn|j|dkr||dkr|||tdt|dd||j|<d S) aH 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'} z%Support must be added on a known noder;r<r=rr>r?r@N)r r"r.rrBrrArL)rrItyperrr apply_support s"  zTruss.apply_supportcCs||jvr td|t|jvrtd|j|dkr:||tdt|dd||tdt|ddn|j|d krP||tdt|dd|j|d S) a4 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 {} z No such node exists in the Trussz+No support has been added to the given noder;r<r=rr>r?r@N)r r"r.rrLrrAr/)rrIrrrremove_support5s  zTruss.remove_supportN)__name__ __module__ __qualname____doc__rpropertyrrrrrrrr r!r(r3r8r9rFrGrBrLrNrOrrrrr s>#         +/+#Y,-2 *rN)rSsympy.core.symbolrsympy.core.sympifyrrrrrrs