HP 48gII Graphing Calculator Manual do Utilizador descarregar pdf (Página 217)

100

101

Page 6-16

• 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













zzzyzx

yzyyyx

xzxyxx

σσσ

The equation is

,)]([

zzyyxxxx

∆⋅++⋅−= ασσσ here e

is the unit

strain in the x-direction, σ

, σ

, and σ

, 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: σ

= 2500 psi, σ

=1200 psi,

and σ

= 500 psi, E = 1200000 psi, n = 0.15, α = 0.00001/

F, ∆T = 60

To calculate the strain e

use the following:

‚Ï@@OK@@ Access numerical solver to solve equations

‚O Access the equation writer to enter equation

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