ࡱ> /1. xbjbjss ;J n n 8det)B0  "e#<# AAAAAAAYCEA-$""$$A A***$<  A*$A**8<0kJ= O/N%6h=AA0)B~=^G'JG,=G=#0#"*$/$d###AAO)6###)B$$$$G#########n w: Multiple-Choice Test Chapter 08.07 Finite Difference Method The exact solution to the boundary value problem  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3  for  EMBED Equation.3  is  EMBED Equation.3  0.00 16.000 37.333 Given  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3  the value of  EMBED Equation.3  at  EMBED Equation.3  using the finite difference method and a step size of  EMBED Equation.3  can be approximated by  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Given  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , the value of  EMBED Equation.3  using the finite difference method with a second order accurate central divided difference method and a step size of  EMBED Equation.3  is 0.000 37.333  EMBED Equation.3   EMBED Equation.3  The transverse deflection  EMBED Equation.3  of a cable of length  EMBED Equation.3  that is fixed at both ends, is given as a solution to  EMBED Equation.3  where  EMBED Equation.3  = tension in cable  EMBED Equation.3  = flexural stiffness  EMBED Equation.3  = distributed transverse load  EMBED Word.Picture.8  Given  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , and  EMBED Equation.3   SHAPE \* MERGEFORMAT Using finite difference method modeling with second order central divided difference accuracy and a step size of  EMBED Equation.3 , the value of the deflection at the center of the cable most nearly is 0.0727373 0.0808323 0.0813803 0.0848433 The radial displacement u of a pressurized hollow thick cylinder (inner radius = 53 , outer radius = 83 ) is given at different radial locations. Radius (in)Radial Displacement (in)5.00.00387315.60.00361656.20.00342226.80.00327437.40.00316188.00.0030769 The maximum normal stress, in psi, on the cylinder is given by  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  The maximum stress, in psi, with second order accuracy is 2079.6 2104.5 2130.7 2182.0 For a simply supported beam (at  EMBED Equation.3  and  EMBED Equation.3 ) with a uniform load q, the vertical deflection  EMBED Equation.3  is described by the boundary value ordinary differential equation as  EMBED Equation.3 ,  EMBED Equation.3  where  EMBED Equation.3  = Youngs modulus of the beam  EMBED Equation.3  = second moment of area This ordinary differential equation is based on assuming that  EMBED Equation.3  is small. If  EMBED Equation.3  is not small, then the ordinary differential equation is given by  EMBED Word.Picture.8   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  For a complete solution, refer to the links at the end of the book.     08.07. 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