HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 217

• The user then highlights the field corresponding to the unknown for which to solve the equation, and presses @SOLVE@ • The user may force a solution by providing an initial guess for the solution in the appropriate input field before solving the equation. The calculator uses a search algorithm to pinpoint an interval for which the function changes sign, which indicates the existence of a root or solution. It then utilizes a numerical method to converge into the solution. The solution the calculator seeks is determined by the initial value present in the unknown input field. If no value is present, the calculator uses a default value of zero. Thus, you can search for more than one solution to an equation by changing the initial value in the unknown input field. Examples of the equations solutions are shown following. Example 1 - Hooke's law for stress and strain The equation to use is Hooke's law for the normal strain in the x-direction for a solid particle subjected to a state of stress given by xx yx σ xy σ yy σ σ xz yz    σ zx σ zy σ zz  The equation is exx = 1 E [σ xx − n ⋅ (σ yy + σ zz T , here exx is the unit strain in the x-direction, σxx, σyy, and σzz, are the normal stresses on the particle in the directions of the x-, y-, and z-axes, E is Young's modulus or modulus of elasticity of the material, n is the Poisson ratio of the material, α is the thermal expansion coefficient of the material, and ∆T is a temperature increase. Suppose that you are given the following data: σxx= 2500 psi, σyy =1200 psi, and σzz = 500 psi, E = 1200000 psi, n = 0.15, α = 0.00001/oF, ∆T = 60 oF. To calculate the strain exx use the following: ,Ï@@OK@@ ,O Access numerical solver to solve equations Access the equation writer to enter equation Page 6-16