Solving a System of Three Equations in Three Variables

When designing a product, you may come across a system of equations to be solved. Whatever these equations (linear or not), the 3DEXPERIENCE provides you with resolution methods. These methods are the Simulated Annealing algorithm and the SetOfEquations capability. This task shows you how to use a system of three equations in three variables.

This task shows you how to:

Solve the System of Equations Using the Simulated Annealing Algorithm

You can solve the system of equations using the simulated annealing algorithm.

  1. Create a 3D Shape.
  2. From the Tools section, click Formula and create six real type parameters. Assign a name to these parameters: x1, y1, z1 and x2, y2, z2.
  3. From the Compass, click 3D Modeling Apps and select Design Optimization, and click Optimization .
  4. In the Constraints tab, specify the three constraints (enter the constraints one by one) x1 + y1 - z1 == 0 x1*y1 - z1 == 0 sin(x1*1rad)**2 - y1 - 1 == 0 . For more information, see the Design Optimization User's Guide.
    1. Enter x1 + y1 - z1 == 0
    2. Enter x1*y1 - z1 == 0
    3. Enter sin(x1*1rad)**2 - y1 - 1 == 0
    4. Specify a precision of 0.01 for all three constraints.
  5. In the Problem tab, click Edit List to specify x1, y1, z1 as free parameters.
  6. Click Edit ranges and step to specify the step value, 1 in this example.
  7. Select Only Constraints from the Optimization type list.
  8. Run the optimization process in Simulated Annealing Algorithm mode. You can use the default termination criteria.
    After the process has finished running, the x1, y1 and z1 values are close to the one below:

    x1 = 0.454

    y1 = -0.807

    z1 = -0.363

Keep your 3D Shape open and proceed to the next section.

Solve the System of Equations Using the "SetOfEquations" Capability

You can solve the system of equations using the SetOfEquations capability.

  1. From the Compass, click 3D Modeling Apps select Engineering Rules Capture, and click Set of Equations .
  2. In the Set of Equations editor, enter the following of equations below: x2 + y2 == z2 ; x2*y2 == z2; sin(x2*1rad)**2 == y2 +1
  3. Specify x2, y2 and z2 as Unknown parameters using the Parse arrow.
  4. Click Solve and OK when done.
    The system of equations is solved and the values are displayed in the tree .