o o h U@sndZddlmZddlmZddlmZmZmZm Z m Z ddl m Z ddl mZddlmZGdd d Zd S) zA This module can be used to solve problems related to 2D Cables. )sympify)Symbol)sincospiatandiff)sqrt)linsolve)Matrixc@seZdZdZddZeddZeddZedd Zed d Z ed d Z eddZ eddZ eddZ ddZddZddZddZddZddZd S)!Cablea Cables are structures in engineering that support the applied transverse loads through the tensile resistance developed in its members. Cables are widely used in suspension bridges, tension leg offshore platforms, transmission lines, and find use in several other engineering applications. Examples ======== A cable is supported at (0, 10) and (10, 10). Two point loads acting vertically downwards act on the cable, one with magnitude 3 kN and acting 2 meters from the left support and 3 meters below it, while the other with magnitude 2 kN is 6 meters from the left support and 6 meters below it. >>> from sympy.physics.continuum_mechanics.cable import Cable >>> c = Cable(('A', 0, 10), ('B', 10, 10)) >>> c.apply_load(-1, ('P', 2, 7, 3, 270)) >>> c.apply_load(-1, ('Q', 6, 4, 2, 270)) >>> c.loads {'distributed': {}, 'point_load': {'P': [3, 270], 'Q': [2, 270]}} >>> c.loads_position {'P': [2, 7], 'Q': [6, 4]} cCsg|_g|_i|_g|_iid|_i|_d|_i|_i|_t d|_ |d|dkr/t d|d|dkr;t dt |d}t |d}||g|j|d<t |d}t |d}||g|j|d<|d|dkr|j ||j ||j ||j ||j |d|j |dn(|j ||j ||j ||j ||j |d|j |d|jD]}d|jt d|d<d|jt d|d <qd S) a Initializes the class. Parameters ========== support_1 and support_2 are tuples of the form (label, x, y), where label : String or symbol The label of the support x : Sympifyable The x coordinate of the position of the support y : Sympifyable The y coordinate of the position of the support ) distributed point_loadrz$Supports can not have the same labelz(Supports can not be at the same locationR__x_yN) _left_support_right_support _supports_support_labels_loads_loads_position_length_reaction_loads_tensionr_lowest_x_global ValueErrorappendr)self support_1 support_2x1y1x2y2ir({/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/physics/continuum_mechanics/cable.py__init__)sJ               zCable.__init__cC|jS)zW Returns the supports of the cable along with their positions. )rr r(r(r)supportsizCable.supportscCr+)z; Returns the position of the left support. )rr,r(r(r) left_supportqzCable.left_supportcCr+)z< Returns the position of the right support. )rr,r(r(r) right_supportxr0zCable.right_supportcCr+)z_ Returns the magnitude and direction of the loads acting on the cable. )rr,r(r(r)loadsr.z Cable.loadscCr+)zV Returns the position of the point loads acting on the cable. )rr,r(r(r)loads_positionr.zCable.loads_positioncCr+)z2 Returns the length of the cable. )rr,r(r(r)lengthr0z Cable.lengthcCr+)zb Returns the reaction forces at the supports, which are initialized to 0. )rr,r(r(r)reaction_loadsr.zCable.reaction_loadscCr+)z^ Returns the tension developed in the cable due to the loads applied. )rr,r(r(r)tensionr.z Cable.tensioncCs`d|jvr td||jdks||jdkrtd|jd}td}||||jiS)zf Returns the tension at a given value of x developed due to distributed load. r z4No distributed load added or solve method not calledrz1The value of x should be between the two supportsX)rkeysrrrrsubsr)r xAr7r(r(r) tension_ats zCable.tension_atcCsN|jd|jdd|jd|jddd}||kr"td||_dS)a This method specifies the length of the cable Parameters ========== length : Sympifyable The length of the cable Examples ======== >>> from sympy.physics.continuum_mechanics.cable import Cable >>> c = Cable(('A', 0, 10), ('B', 10, 10)) >>> c.apply_length(20) >>> c.length 20 rrrg?z@length should not be less than the distance between the supportsN)rrrr)r r4distr(r(r) apply_lengths zCable.apply_lengthc Cs||jvr td|j|}|j|dd}|j|d}|j|d}t|d}t|d}|jD]} | dt||ksI| dt||krMtdq5|j||j |j |j |j |||g|j|d<||kr|j ||j ||j ||j ||j|dn!|j ||j ||j ||j ||jd|d|jD]}d|j td|d<d|j td|d<qd S) a^ This method changes the mentioned support with a new support. Parameters ========== label: String or symbol The label of the support to be changed new_support: Tuple of the form (new_label, x, y) new_label: String or symbol The label of the new support x: Sympifyable The x-coordinate of the position of the new support. y: Sympifyable The y-coordinate of the position of the new support. Examples ======== >>> from sympy.physics.continuum_mechanics.cable import Cable >>> c = Cable(('A', 0, 10), ('B', 10, 10)) >>> c.supports {'A': [0, 10], 'B': [10, 10]} >>> c.change_support('B', ('C', 5, 6)) >>> c.supports {'A': [0, 10], 'C': [5, 6]} z&No support exists with the given labelrrrz>The change in support will throw an existing load out of rangerrrN)rrrindexrrmaxminpoprclearrrremoverinsertr) r label new_supportr' rem_labelr#r$r:ylr(r(r)change_supportsB     $              zCable.change_supportcCs|dkr\t|jddkrtd|d}||jdvr tdt|d}t|d}||jdks:||jdkr>td t|d }t|d }||g|jd|<||g|j|<dS|dkrt|jdkrktd |d}||jdvrztdt|d}||jd|<dStd )a This method adds load to the cable. Parameters ========== order : Integer The order of the applied load. - For point loads, order = -1 - For distributed load, order = 0 load : tuple * For point loads, load is of the form (label, x, y, magnitude, direction), where: label : String or symbol The label of the load x : Sympifyable The x coordinate of the position of the load y : Sympifyable The y coordinate of the position of the load magnitude : Sympifyable The magnitude of the load. It must always be positive 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. * For uniformly distributed load, load is of the form (label, magnitude) label : String or symbol The label of the load magnitude : Sympifyable The magnitude of the load. It must always be positive Examples ======== For a point load of magnitude 12 units inclined at 30 degrees with the horizontal: >>> from sympy.physics.continuum_mechanics.cable import Cable >>> c = Cable(('A', 0, 10), ('B', 10, 10)) >>> c.apply_load(-1, ('Z', 5, 5, 12, 30)) >>> c.loads {'distributed': {}, 'point_load': {'Z': [12, 30]}} >>> c.loads_position {'Z': [5, 5]} For a uniformly distributed load of magnitude 9 units: >>> from sympy.physics.continuum_mechanics.cable import Cable >>> c = Cable(('A', 0, 10), ('B', 10, 10)) >>> c.apply_load(0, ('X', 9)) >>> c.loads {'distributed': {'X': 9}, 'point_load': {}} r rzDistributed load already existsrzLabel already existsrrz2The load should be positioned between the supportszPoint load(s) already existzOrder should be either -1 or 0N)lenrrrrrr)r orderloadrFr:rI magnitude directionr(r(r) apply_loads.A     zCable.apply_loadcGs|D]>}t|jdkr#||jdvrtd|d|jd|q||jdvr2td|d|jd||j|qdS)an This methods removes the specified loads. Parameters ========== This input takes multiple label(s) as input label(s): String or symbol The label(s) of the loads to be removed. Examples ======== >>> from sympy.physics.continuum_mechanics.cable import Cable >>> c = Cable(('A', 0, 10), ('B', 10, 10)) >>> c.apply_load(-1, ('Z', 5, 5, 12, 30)) >>> c.loads {'distributed': {}, 'point_load': {'Z': [12, 30]}} >>> c.remove_loads('Z') >>> c.loads {'distributed': {}, 'point_load': {}} rr zError removing load z: no such load exists disrtibutedrN)rOrrrrB)r argsr'r(r(r) remove_loads|szCable.remove_loadsc Gsh t|jdkrTt|jddd}||jd|d|jd|jd}d}d}d}d|_ t dt|dD]L}|dkrp|j t |j d|j||ddd|j d|j||ddd7_ n;|j t |j||ddd|j||ddd|j||ddd|j||ddd7_ |t|dkr|j t |j d|j||ddd|j d|j||ddd7_ ||jd||ddtt|jd||dddt|j d|j||dd7}||jd||ddtt|jd||dddt|j d|j||dd7}||jd||ddtt|jd||ddd7}||jd||ddtt|jd||ddd7}t||dd ||dd}|j||dd} |j||dd} d} d} |t|dkr|j d} |j d} n|j||ddd} |j||ddd} t| | | | } | t|j d|j||ddt| t|j d|j||ddt| }||j|<||jd||ddtt|jd||dddt|j d|j||dd7}||jd||ddtt|jd||dddt|j d|j||dd7}q=t|ddd |dd}|j|ddd} |j|ddd} |j d} |j d} t| | | |  } | t|j d|j|dddt| t|j d|j|dddt| }||j|<td| } |jd}t|  ||jtd |d <|t|  |7}t| ||jtd |d <|t| |7}|jd}| |jtd |d <| |jtd |d <dSt|jd dkrt|dkritdt|d}t|d}||_td}td}td}t|j dd|j dd|j dg|j dd|j dd|j dg|d|d|gg}tt||||f}t|dkrtd|dd}|dd}|dd}td}td}|||d|||||}t|jd }|d}||j d|dd|j d|}|jt||}|tt||jd <|jd}||j dtt|||j d||jtd |d <||j dtt|||j d||jtd |d <|jd}||j dtt|||j d||jtd |d <||j dtt|||j d||jtd |d <dSdS)aU This method solves for the reaction forces at the supports, the tension developed in the cable, and updates the length of the cable. Parameters ========== This method requires no input when solving for point loads For distributed load, the x and y coordinates of the lowest point of the cable are required as x: Sympifyable The x coordinate of the lowest point y: Sympifyable The y coordinate of the lowest point Examples ======== For point loads, >>> from sympy.physics.continuum_mechanics.cable import Cable >>> c = Cable(("A", 0, 10), ("B", 10, 10)) >>> c.apply_load(-1, ('Z', 2, 7.26, 3, 270)) >>> c.apply_load(-1, ('X', 4, 6, 8, 270)) >>> c.solve() >>> c.tension {A_Z: 8.91403453669861, X_B: 19*sqrt(13)/10, Z_X: 4.79150773600774} >>> c.reaction_loads {R_A_x: -5.25547445255474, R_A_y: 7.2, R_B_x: 5.25547445255474, R_B_y: 3.8} >>> c.length 5.7560958484519 + 2*sqrt(13) For distributed load, >>> from sympy.physics.continuum_mechanics.cable import Cable >>> c=Cable(("A", 0, 40),("B", 100, 20)) >>> c.apply_load(0, ("X", 850)) >>> c.solve(58.58, 0) >>> c.tension {'distributed': 36456.8485*sqrt(0.000543529004799705*(X + 0.00135624381275735)**2 + 1)} >>> c.tension_at(0) 61709.0363315913 >>> c.reaction_loads {R_A_x: 36456.8485, R_A_y: -49788.5866682485, R_B_x: 44389.8401587246, R_B_y: 42866.621696333} rcSs |ddS)Nrrr()itemr(r(r)s zCable.solve..)keyrrr_rrrr z%Provide the lowest point of the cableabcz2The lowest point is inconsistent with the supportsr7YN) rOrsorteditemsrrrErrCrranger rrrrrabsrrrrrrrr listr valuesrr<r9)r rVsorted_positionmoment_sum_from_left_supportmoment_sum_from_right_supportF_xF_yr'rFr&r%r$r#angle_with_horizontalr6lowest_xlowest_yr]r^r_Mcoefficient_solutionr;BCr7r` temp_list applied_forcehorizontal_force_constanttangent_slope_to_curver(r(r)solves/ XvVhhDD$  ^ hj   ^            $(   @@ @Dz Cable.solveN)__name__ __module__ __qualname____doc__r*propertyr-r/r1r2r3r4r5r6r<r>rKrTrWrwr(r(r(r)r s2@        Gd &r N)r{sympy.core.sympifyrsympy.core.symbolrsympyrrrrr(sympy.functions.elementary.miscellaneousr sympy.solvers.solvesetr sympy.matricesr r r(r(r(r)s