/* * A Java Applet Used to Draw Mohr's Circle in a Plane for Stress Analysis * found at: http://www.aoe.vt.edu/~jing/MohrCircle.html * This Java applet can be used to draw Mohr's circle and stress analysis * in a Plane. It is used for educational purpose. * */ import java.awt.*; import java.applet.*; public class Mohr extends Applet { int xp = 0; int yp = 0; double dsigma_x; double dsigma_y; double dtau_xy; double dradius; double dsigma_ave; double dsigma_1; double dsigma_2; double dtheta_p; double dsigma_mis; String filled; MohrControls controls; public void init() { setLayout(new BorderLayout()); MohrCanvas c = new MohrCanvas(); add("Center", c); add("South", controls = new MohrControls(c)); } public void start() { controls.enable(); } public void stop() { controls.disable(); } public boolean handleEvent(Event e) { if (e.id == Event.WINDOW_DESTROY) { System.exit(0); } return false; } public static void main(String args[]) { Frame f = new Frame("Mohr's Circle"); Mohr mohr = new Mohr(); mohr.init(); mohr.start(); f.add("Center", mohr); f.resize(543, 363); f.show(); } } class MohrCanvas extends Canvas { int radius = 0; int xx = 0; int yy = 0; double drr; double dxx; double dyy; double dsigma_x; double dsigma_y; double dtau_xy; double dradius; double dsigma_ave; double dsigma_1; double dsigma_2; double dtheta_p; double dsigma_mis; String filled = "draw"; Font font; int xp ; int yp; public void paint(Graphics g) { Rectangle r = bounds(); int glines = 1; int dlines = 15; int hlines = r.height / glines; int vlines = r.width / glines; int two_x_0 = vlines * glines; int two_y_0 = hlines * glines; /* * Draw grid lines as a bacground of the window * * * g.setColor(Color.pink); * for (int i = 1; i <= hlines / 2 +1; i++) { * g.drawLine(0, two_y_0 / 2 + i * glines, two_x_0 , * two_y_0 / 2 + i * glines); * g.drawLine(0, two_y_0 / 2 - i * glines, two_x_0 , * two_y_0 / 2 - i * glines); * } * for (int i = 1; i <= vlines / 2 +1; i++) { * g.drawLine(two_x_0 / 2 + i * glines, 0, * two_x_0 / 2 + i * glines, two_y_0); * g.drawLine(two_x_0 / 2 - i * glines, 0, * two_x_0 / 2 - i * glines, two_y_0); * } */ /* * Calculate the scaled data for Mohr's circle and the unit per division */ double dunit = 1.0d; double dscalar = 1.0d; drr = dradius * ((double)dlines / dunit); dxx = dsigma_ave * ((double)dlines / dunit); dyy = 0.0d; double dsigxx = dsigma_x * ((double)dlines / dunit); double dsigyy = dsigma_y * ((double)dlines / dunit); double dtauxy = dtau_xy * ((double)dlines / dunit); if(drr >= (double)dlines) { dscalar = 10.0d; } else { dscalar = 0.1d; } if(drr > 1.e-300) {while(2.0d * drr > (double)r.height - 30.0d){ dunit = dscalar * dunit; drr = drr / dscalar; dxx = dxx / dscalar; dsigxx = dsigxx / dscalar; dsigyy = dsigyy / dscalar; dtauxy = dtauxy / dscalar; } } if(drr > 1.e-300 ) {while(drr < (double)dlines){ dunit = dscalar * dunit; drr = drr / dscalar; dxx = dxx / dscalar; dsigxx = dsigxx / dscalar; dsigyy = dsigyy / dscalar; dtauxy = dtauxy / dscalar; } } double km = 1.0d; if(filled.equals("size 1")) { if(4 * (int)drr <= r.height ) { dlines = 2 * dlines; km = 2.0d; } } if(filled.equals("size 2")) { if(8 * (int)drr <= r.height ) { dlines = 4 * dlines; km = 4.0d; } else { if(4 * (int)drr <= r.height ) { dlines = 2 * dlines; km = 2.0d; } } } radius = (int)(km * drr); xx = (int)(km * dxx); yy = 0; int sxx = (int)(km * dsigxx); int syy = (int)(km * dsigyy); int txy = (int)(km * dtauxy); int nxxoff = 0; while( 2 * (xx + radius) > r.width - 90) { xx = xx - dlines; sxx = sxx - dlines; syy = syy - dlines; nxxoff = nxxoff + 1; } while( 2 * (xx - radius) < - r.width) { xx = xx + dlines; sxx = sxx + dlines; syy = syy + dlines; nxxoff = nxxoff - 1; } /* * Draw Mohr's circle, filled or not */ g.setColor(Color.red); if (filled.equals("Fill")) { g.fillArc(two_x_0 / 2-radius+xx, two_y_0 / 2 -radius-yy, radius+radius, radius+radius, 0, 360); } else { g.drawArc(two_x_0 / 2-radius+xx, two_y_0 / 2 -radius-yy, radius+radius, radius+radius, 0, 360); } g.setColor(Color.green); g.fillArc(two_x_0 / 2-radius+xx, two_y_0 / 2 -radius-yy, radius+radius, radius+radius, 0, -2 * (int)dtheta_p); g.drawLine(two_x_0 / 2+sxx, two_y_0 / 2 +txy, two_x_0 / 2+syy , two_y_0 / 2 -txy); g.setColor(Color.blue); g.drawOval(two_x_0 / 2+xx-radius-2, two_y_0 / 2-2, 4, 4); g.drawOval(two_x_0 / 2+xx+radius-2, two_y_0 / 2-2, 4, 4); g.drawOval(two_x_0 / 2+xx-2, two_y_0 / 2 +radius-2, 4, 4); g.drawOval(two_x_0 / 2+xx-2, two_y_0 / 2 -radius-2, 4, 4); g.drawOval(two_x_0 / 2+xx-2, two_y_0 / 2 -2, 4, 4); g.setColor(Color.white); g.drawOval(two_x_0 / 2+sxx-2, two_y_0 / 2 -txy-2, 4, 4); g.drawOval(two_x_0 / 2+syy-2, two_y_0 / 2 -txy-2, 4, 4); g.drawOval(two_x_0 / 2+sxx-2, two_y_0 / 2 +txy-2, 4, 4); g.drawOval(two_x_0 / 2+syy-2, two_y_0 / 2 +txy-2, 4, 4); /* * Draw axis lines with the center of the window as origin */ g.setColor(Color.black); g.drawLine(0, two_y_0 / 2, two_x_0 , two_y_0 / 2); g.drawLine(two_x_0 / 2, 0, two_x_0 / 2, two_y_0); /* * Draw disivion lines/points along axises */ g.setColor(Color.pink); for (int i = 1; i <= hlines / 2 +1; i++) { g.drawLine(0, two_y_0 / 2 + i * dlines, two_x_0 , two_y_0 / 2 + i * dlines); g.drawLine(0, two_y_0 / 2 - i * dlines, two_x_0 , two_y_0 / 2 - i * dlines); } for (int i = 1; i <= vlines / 2 +1; i++) { g.drawLine(two_x_0 / 2 + i * dlines, 0, two_x_0 / 2 + i * dlines, two_y_0); g.drawLine(two_x_0 / 2 - i * dlines, 0, two_x_0 / 2 - i * dlines, two_y_0); } g.setColor(Color.black); for (int i = 1; i <= hlines / 2 +1; i++) { g.drawLine(two_x_0 / 2, two_y_0 / 2 + i * dlines, two_x_0 / 2 + 2, two_y_0 / 2 + i * dlines); g.drawLine(two_x_0 / 2, two_y_0 / 2 - i * dlines, two_x_0 / 2 + 2, two_y_0 / 2 - i * dlines); } for (int i = 1; i <= vlines / 2 +1; i++) { g.drawLine(two_x_0 / 2 + i * dlines, two_y_0 / 2 , two_x_0 / 2 + i * dlines, two_y_0 / 2 - 2); g.drawLine(two_x_0 / 2 - i * dlines, two_y_0 / 2 , two_x_0 / 2 - i * dlines, two_y_0 / 2 - 2); } g.setColor(Color.darkGray); for (int i = 1; i <= hlines / dlines +3; i++) { g.drawString(""+i,two_x_0/2 - 12,two_y_0 / 2 - i * dlines ); } for (int i = 1; i <= vlines / dlines +4; i++) { g.drawString(""+(i + nxxoff),two_x_0 / 2 + i * dlines, two_y_0/2 - 3); } /* * Draw data for Mohr's circle and stresses onto the window */ g.setColor(Color.darkGray); g.drawString("sigma x " + dunit ,two_x_0 - 105, two_y_0 / 2 + 12 ); g.drawString("tau x " + dunit ,two_x_0/2 + 6, 12 ); g.drawString("O(" + nxxoff + ",0)",two_x_0/2 + 6,two_y_0 / 2 + 12 ); g.setColor(Color.white); g.drawString("Input Stresses:",10,12); g.drawString("sigma_x = " + dsigma_x,10,27); g.drawString("sigma_y = " + dsigma_y,10,42); g.drawString("tau_xy = " + dtau_xy,10,57); g.setColor(Color.blue); g.drawString("Mohr's Circle: ",10,87); g.drawString("sigma_ave = " + dsigma_ave,10,102); g.drawString("radius = " + dradius,10,117); g.drawString("Principal Stresses:",10,two_y_0 / 2 + 12); g.drawString("sigma_1 = " + dsigma_1,10,two_y_0 / 2 + 27); g.drawString("sigma_2 = " + dsigma_2,10,two_y_0 / 2 + 42); g.drawString("theta_p = " + dtheta_p + " deg.",10,two_y_0 / 2 + 57); g.drawString("sigma_mises = " + dsigma_mis,10,two_y_0 / 2 + 72); g.drawString("tau_max = " + dradius,10,two_y_0 / 2 + 87); g.setColor(Color.blue); g.drawString(" sigma_1 ",two_x_0/2 + xx +radius,two_y_0 - 33); g.drawLine(two_x_0 / 2 + xx + radius, two_y_0 - 33, two_x_0 / 2 + xx + radius, two_y_0/ 2); g.drawString(" sigma_2",two_x_0/2 + xx -radius,two_y_0 - 3 ); g.drawLine(two_x_0 / 2 + xx - radius, two_y_0 - 3 , two_x_0 / 2 + xx - radius, two_y_0 / 2); g.drawString("tau_max",two_x_0/2 - 150, two_y_0/2 - radius - 3); g.drawLine(two_x_0 / 2 - 150, two_y_0 / 2 - radius , two_x_0 / 2 + xx, two_y_0 / 2 - radius); g.drawString(" sigma_ave ",two_x_0/2 + xx,two_y_0 - 18); g.drawLine(two_x_0 / 2 + xx, two_y_0 - 18, two_x_0 / 2 + xx, two_y_0 / 2); g.setColor(Color.white); if(sxx <= syy) { g.drawString(" sigma_x",two_x_0/2 + sxx, two_y_0 - 48); g.drawLine(two_x_0 / 2 + sxx, two_y_0 - 48, two_x_0 / 2 + sxx, two_y_0 / 2 - txy); g.drawString(" sigma_y",two_x_0/2 + syy,two_y_0 - 63); g.drawLine(two_x_0 / 2 + syy, two_y_0 - 63, two_x_0 / 2 + syy, two_y_0 / 2 - txy); g.drawString("tau_xy ",two_x_0/2 - 90, two_y_0/2 - txy -3); g.drawLine(two_x_0 / 2 - 90, two_y_0/2 - txy , two_x_0 / 2 + sxx, two_y_0 / 2 - txy); } else { g.drawString(" sigma_x",two_x_0/2 + sxx, two_y_0 - 63); g.drawLine(two_x_0 / 2 + sxx, two_y_0 - 63, two_x_0 / 2 + sxx, two_y_0 / 2 - txy); g.drawString(" sigma_y",two_x_0/2 + syy,two_y_0 - 48); g.drawLine(two_x_0 / 2 + syy, two_y_0 - 48, two_x_0 / 2 + syy, two_y_0 / 2 - txy); g.drawString("tau_xy ",two_x_0/2 - 90, two_y_0/2 - txy -3); g.drawLine(two_x_0 / 2 - 90, two_y_0/2 - txy , two_x_0 / 2 + syy, two_y_0/2 - txy); } g.drawLine(two_x_0 / 2 + sxx, two_y_0/2 - txy , two_x_0 / 2 + syy, two_y_0/2 - txy); double sigma = (double)((int)(100.0d * (double)(xp - two_x_0/2)/(double)dlines)) / 100.0d; double tau = (double)((int)(100.0d * (double)(two_y_0/2 - yp)/(double)dlines)) / 100.0d; g.setColor(Color.red); g.drawString("sigma = " + (dunit * (sigma + nxxoff)),two_x_0 - 115, 12); g.drawString("tau = " + (dunit * tau) ,two_x_0 - 115, 27); g.setColor(Color.green); g.drawString("The green sector has", 10, two_y_0 - 27); g.drawString("an angle of 2 times theta_p.", 10, two_y_0 - 12); } public void redraw(String filled, int xp, int yp, double dsigma_x, double dsigma_y, double dtau_xy, double dradius, double dsigma_ave, double dsigma_1, double dsigma_2, double dtheta_p, double dsigma_mis) { this.filled = filled; this.xp = xp; this.yp = yp; this.dsigma_x = dsigma_x; this.dsigma_y = dsigma_y; this.dtau_xy = dtau_xy; this.dradius = dradius; this.dsigma_ave = dsigma_ave; this.dsigma_1 = dsigma_1; this.dsigma_2 = dsigma_2; this.dtheta_p = dtheta_p; this.dsigma_mis = dsigma_mis; repaint(); } public boolean mouseDown(Event evt, int x, int y){ Rectangle r = bounds(); if(x < r.width) { if ( y < r.height) { xp = x; yp = y; redraw(filled, xp, yp, dsigma_x, dsigma_y, dtau_xy, dradius, dsigma_ave, dsigma_1, dsigma_2, dtheta_p, dsigma_mis); return true; } } return true; } } class MohrControls extends Panel { TextField sigma_xText; TextField sigma_yText; TextField tau_xyText; MohrCanvas canvas; int xp = 0; int yp = 0; double dsigma_x; double dsigma_y; double dtau_xy; double dradius; double dsigma_ave; double dsigma_1; double dsigma_2; double dtheta_p; double dsigma_mis; public MohrControls(MohrCanvas canvas) { this.canvas = canvas; setLayout(new GridLayout(2,7,5,0)); add(sigma_xText = new TextField("0.0", 8)); add(sigma_yText = new TextField("0.0", 8)); add(tau_xyText = new TextField("0.0", 8)); add(new Button("Fill")); add(new Button("Draw")); add(new Button("size 1")); add(new Button("size 2")); add(new Label(" sigma_x")); add(new Label(" sigma_y")); add(new Label(" tau_xy")); add(new Label("")); add(new Label("")); add(new Label(" 2 times")); add(new Label(" 4 times")); } public boolean action(Event ev, Object arg) { if (ev.target instanceof Button) { /* * Get the original stresses for a Mohr's circle */ dsigma_x = (Double.valueOf(sigma_xText.getText().trim())).doubleValue(); dsigma_y = (Double.valueOf(sigma_yText.getText().trim())).doubleValue(); dtau_xy = (Double.valueOf(tau_xyText.getText().trim())).doubleValue(); /* * Calculate the data for Mohr's circle and principal stresses */ dradius = Math.sqrt((dsigma_x - dsigma_y) * (dsigma_x - dsigma_y)/4.0d + dtau_xy * dtau_xy); dsigma_ave = (dsigma_x + dsigma_y)/2.0d; dsigma_1 = dsigma_ave + dradius; dsigma_2 = dsigma_ave - dradius; dtheta_p = (90.0d/Math.PI)*Math.atan(2.0d*dtau_xy/(dsigma_x - dsigma_y)); dsigma_mis = Math.sqrt(dsigma_x * dsigma_x - dsigma_x * dsigma_y + dsigma_y * dsigma_y + 3.0d * dtau_xy * dtau_xy); /* * Draw Mohr's circle and principal stresses onto the window */ canvas.redraw((String)arg, xp, yp, dsigma_x, dsigma_y, dtau_xy, dradius, dsigma_ave, dsigma_1, dsigma_2, dtheta_p, dsigma_mis); return true; } return false; } }