Мещерский задача 4.43 — различия между версиями

Версия 19:50, 8 июня 2017

Мещерский Задача 7.10

Визуализация 3D-задачи по статике на JavaScript

Группа 23604/1 Кафедра Теоретической механики

Формулировка задачи

Подвеска состоит из двух балок AB и CD, соединенных шарнирно в точке D и прикрепленных к потолку шарнирами A и C. Вес балки AB равен 60 Н и приложен в точке E. Вес балки CD равен 50 Н и приложен в точке F. В точке B к балке AB приложена вертикальная сила P=200 Н. Определить реакции в шарнирах A и C, если заданы следующие размеры: AB=1 м; CD=0,8 м; AE=0,4 м; CF=0,4 м; углы наклона балок AB и CD к горизонту соответственно равны: α=60° и β=45°.

Решение задачи

Код

<!DOCTYPE html>

<head>

   <meta charset = "utf-8">
   <script src = "http://tm.spbstu.ru:8090/ws-htmlets/Umanskij_AO/4.43%20%D0%9C%D0%B5%D1%89%D0%B5%D1%80%D1%81%D0%BA%D0%B8%D0%B9/Three.js"></script>
   <script src = "http://tm.spbstu.ru:8090/ws-htmlets/Umanskij_AO/4.43%20%D0%9C%D0%B5%D1%89%D0%B5%D1%80%D1%81%D0%BA%D0%B8%D0%B9/stats.min.js"></script>
   <script src = "http://tm.spbstu.ru:8090/ws-htmlets/Umanskij_AO/4.43%20%D0%9C%D0%B5%D1%89%D0%B5%D1%80%D1%81%D0%BA%D0%B8%D0%B9/OrbitControls.js"></script>
   <script src = "http://tm.spbstu.ru:8090/ws-htmlets/Umanskij_AO/4.43%20%D0%9C%D0%B5%D1%89%D0%B5%D1%80%D1%81%D0%BA%D0%B8%D0%B9/dat.gui.js"></script>
   <style>
   body
   {
      margin:0;
      overflow:hidden;
   }
   </style>

</head> <body>

   <script>
       var renderer, scene, camera, stats, stairs1,stairs2;
       var RA, RAx, RAy, RB, RBx, RBy, P, Pab, Pcd;
       var step = 0;

       var controls = new function()
       {
           this.alpha1 = Math.PI / 3;
     this.alpha2 = Math.PI / 6;
           this.length1 = 4;
     this.length2 = 10;
           this.gamma = 1/2;
     this.Pab = 1;
     this.Pcd = 1;
     this.P = 1;
           this.PositionPab = 1/2;
     this.PositionPcd = 1/2;
   
   }
       var gui = new dat.GUI();
       gui.add(controls, 'alpha1', 0, Math.PI / 2).onChange(Refresh_Scene);
     gui.add(controls, 'alpha2', 0.1, Math.PI / 3).onChange(Refresh_Scene);
       gui.add(controls, 'length1', 1, 10).onChange(Refresh_Scene);
   gui.add(controls, 'gamma', 0, 1).onChange(Refresh_Scene);
   gui.add(controls, 'P', 0, 10).onChange(Refresh_Scene);
   gui.add(controls, 'Pab', 0, 10).onChange(Refresh_Scene);
   gui.add(controls, 'Pcd', 0, 10).onChange(Refresh_Scene);
       gui.add(controls, 'PositionPab', 0, 1).onChange(Refresh_Scene);
   gui.add(controls, 'PositionPcd', 0, 1).onChange(Refresh_Scene);
       function Stairs_Pos()
       {
           scene.remove(stairs1);
     scene.remove(stairs2);
           var stairsM = new THREE.LineBasicMaterial({color: 0x000000});
     var stairs1G = new THREE.Geometry();
           stairs1G.vertices.push(new THREE.Vector3(0, 0, 0));
           stairs1G.vertices.push(new THREE.Vector3(controls.length1 * Math.cos(controls.alpha1), -controls.length1 * Math.sin(controls.alpha1), 0));
           stairs1 = new THREE.Line(stairs1G, stairsM);
           scene.add(stairs1);
     var stairs2G = new THREE.Geometry();
           stairs2G.vertices.push(new THREE.Vector3(controls.gamma * controls.length1 * Math.cos(controls.alpha1),controls.gamma*(-controls.length1 * Math.sin(controls.alpha1)) , 0));
           stairs2G.vertices.push(new THREE.Vector3(controls.gamma * controls.length1 * Math.sin(controls.alpha1) * Math.cos(controls.alpha2)/Math.sin(controls.alpha2), 0, 0));
           stairs2 = new THREE.Line(stairs2G, stairsM);
           scene.add(stairs2);
     
       }

       function Forces_Remove()
       {
           scene.remove(RA);
           scene.remove(RAx);
           scene.remove(RAy);
           scene.remove(RB);
           scene.remove(RBx);
           scene.remove(RBy);
           scene.remove(P);
     scene.remove(Pab);
     scene.remove(Pcd);
       }

       function Forces_Push()
       {
           scene.add(RA);
           scene.add(RAx);
           scene.add(RAy);
           scene.add(RB);
           scene.add(RBx);
           scene.add(RBy);
           scene.add(P);
     scene.add(Pab);
     scene.add(Pcd);
       }

       function Forces_Pos()
       {   var DB = (1-controls.gamma) * controls.length1;
       var DE = (controls.gamma - (-controls.PositionPab)) * controls.length1;
     var AD = controls.gamma * controls.length1;
     var CD = controls.length1 * controls.gamma * Math.sin(controls.alpha1)/Math.sin(controls.alpha2);
     var DK = AD * Math.sin(controls.alpha1)
           var DF = CD *(1- controls.PositionPcd);
     var yC = ((-controls.Pab * DE + controls.P * DB +(controls.Pab+controls.Pcd+controls.P) * AD) * Math.cos(controls.alpha1) + controls.Pcd * DF * Math.cos(controls.alpha2))/(CD * Math.cos(controls.alpha2) + AD * Math.cos(controls.alpha1)) ;
           var yA = controls.Pab + controls.Pcd + controls.P - yC;
     var xA = (-yA * AD *Math.cos(controls.alpha1) + controls.Pab * DE * Math.cos(controls.alpha1) - controls.P * DB * Math.cos(controls.alpha1))/(AD * Math.tan(controls.alpha1));
           var xC = -xA;
           var Nbx = 1 * 1;
           var Nay = 1 * Nbx;
           var Ra = Math.sqrt(xA * xA + yA * yA);
           var Rb = Math.sqrt(xC * xC + yC * yC);
           var lp = controls.length1 * 1 * (1 + Math.tan(controls.alpha1)) / (1 + 1 * 1);

           var headLength = 0.15;
           var headWidth = 0.1;
           var Xpab = controls.gamma * controls.length1 * Math.cos(controls.alpha1)-(1-controls.PositionPcd)*(controls.gamma * controls.length1 * Math.cos(controls.alpha1)-controls.gamma * controls.length1 * Math.sin(controls.alpha1) * Math.cos(controls.alpha2)/Math.sin(controls.alpha2)) 
     
     
     
           Forces_Remove();

           RA = new THREE.ArrowHelper(new THREE.Vector3(xA, yA, 0).normalize(), new THREE.Vector3(0, 0, 0), Ra, 0xFF0000, headLength, headWidth);
           RAx = new THREE.ArrowHelper(new THREE.Vector3(-1, 0, 0), new THREE.Vector3(0, 0, 0), -xA, 0xFF0000, headLength, headWidth);
           RAy = new THREE.ArrowHelper(new THREE.Vector3(0, 1, 0), new THREE.Vector3(0, 0, 0), yA, 0xFF0000, headLength, headWidth);

           RB = new THREE.ArrowHelper(new THREE.Vector3(xC, yC, 0).normalize(), new THREE.Vector3(controls.gamma * controls.length1 * Math.sin(controls.alpha1) * Math.cos(controls.alpha2)/Math.sin(controls.alpha2), 0, 0), Rb, 0xFF0000, headLength, headWidth);
           RBx = new THREE.ArrowHelper(new THREE.Vector3(1, 0, 0), new THREE.Vector3(controls.gamma * controls.length1 * Math.sin(controls.alpha1) * Math.cos(controls.alpha2)/Math.sin(controls.alpha2), 0, 0), xC, 0xFF0000, headLength, headWidth);
           RBy = new THREE.ArrowHelper(new THREE.Vector3(0, 1, 0), new THREE.Vector3(controls.gamma * controls.length1 * Math.sin(controls.alpha1) * Math.cos(controls.alpha2)/Math.sin(controls.alpha2), 0, 0), yC, 0xFF0000, headLength, headWidth);

           P = new THREE.ArrowHelper(new THREE.Vector3(0, -1, 0), new THREE.Vector3(controls.length1 * Math.cos(controls.alpha1), -controls.length1 * Math.sin(controls.alpha1), 0), controls.P, 0xFF0000, headLength, headWidth);

           Pab = new THREE.ArrowHelper(new THREE.Vector3(0, -1, 0), new THREE.Vector3(controls.length1 * Math.cos(controls.alpha1)*controls.PositionPab, -controls.length1 * Math.sin(controls.alpha1)*controls.PositionPab, 0), controls.Pab, 0xFF0000, headLength, headWidth);
     
     Pcd = new THREE.ArrowHelper(new THREE.Vector3(0, -1, 0), new THREE.Vector3( Xpab,controls.gamma*(-controls.length1 * Math.sin(controls.alpha1))*controls.PositionPcd, 0), controls.Pcd, 0xFF0000, headLength, headWidth);
     
     
     
     Forces_Push();
       }

       function Refresh_Scene()
       {
           Stairs_Pos();
           Forces_Pos();
       }

       function init()
       {
           scene = new THREE.Scene();

           camera = new THREE.PerspectiveCamera(60, window.innerWidth/window.innerHeight, 0.1, 1000);

           renderer = new THREE.WebGLRenderer();
           renderer.setClearColor(0xEEEEEE, 1.0);
           renderer.setSize(window.innerWidth, window.innerHeight);

           var axes = new THREE.AxisHelper(20);
           scene.add(axes);

           Refresh_Scene();

           camera.position.x = 0;
           camera.position.y = 0;
           camera.position.z = 10;
           camera.lookAt(0, 0, 0);

           document.getElementById("WebGL").appendChild(renderer.domElement);

           controls1 = new THREE.OrbitControls(camera, renderer.domElement);

           stats = initStats();
           RenderScene();
       };

       function RenderScene()
       {
           stats.update();
           requestAnimationFrame(RenderScene);

           renderer.render(scene,camera);
       }

       function initStats()
       {
           stats = new Stats();
           stats.setMode(0);
           stats.domElement.style.position = '0px';
           stats.domElement.style.left = '0px';
           stats.domElement.style.top = '0px';
           document.getElementById("Stats-output").appendChild(stats.domElement);
           return stats;
       }

       window.onload = init;
   </script>

</body>

@@ Строка 15: / Строка 15: @@
 {{#widget:Iframe |url=http://tm.spbstu.ru:8090/ws-htmlets/Umanskij_AO/4.43/4.43.html |width=1000 |height=830 |border=0 }}
+==Код==
 <div class="mw-collapsible mw-collapsed" style="width:100%" >
 <syntaxhighlight lang="javascript" line start="1" enclose="div">
 <!DOCTYPE html>

Мещерский задача 4.43 — различия между версиями

Версия 19:50, 8 июня 2017

Формулировка задачи

Решение задачи

Код

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