教程5.13g加密所屬nastran學(xué)習(xí)

1、SECTION 14BASIC CONCEPTS OF EULERBASIC CONCEPTSDiscretize the spatial part of the problem by volume elements.Mesh is fixed in time and space.Constant volume elementGrid points have no degree of freedomMaterial moves from element to element.EQUATIONS SOLVED BY EULERIn Eulerian domain the material sta

2、te is defined by the following four variables: : velocity at point P and time t(P,t): density at point P and time te (P,t): specific internal energy at point P and time tij(P): stress tensor at point P and time tFour equations relates these variables to each other:conservation of mass continuitycons

3、ervation of momentum 2nd dynamic lawconservation of energy 1st thermodynamic principleequations of stateConstitutive equation p = (e)stress_strain relationsplasticityfailureEULERIAN IMPLEMENTATION IN MSC.DYTRANControl volume methodThe solution in space is computed using a control volume method.Time

4、integrationThe solution in time is computed using an explicit central finite difference method.The same integration scheme is used as for LagrangeCONTROL VOLUME IMPLEMENTATIONUse Eulerian elements as the control volumes.Mass, velocity, internal energy and stresses are defined at element center and a

5、re constant across an element.Integrate over faces of Eulerian elements.One 1-point approximation at the mid of the face is used to evaluate the surface integrals.The ”face values” are found from averaging of the values of the center of the elements adjacent to a face.This simple averaging makes the

6、 implementation first order accurate.Face values are needed for:transport (velocity over face)impulse on element mass, work on element massADVANTAGES OF CONTROL VOLUME METHODSAllows severe deformations since the material can freely flow inside the Eulerian mesh.Eliminates tedious meshing operations.

7、Prevents small time steps by eliminating the construction of fine mesh or small elements.FIRST ORDER COMPUTATIONAL CYCLETIMESTEP CALCULATIONCourant criterionThe timestep is computed according the Courant Criterion, which is based on the minimum time for a stress wave to cross on an element.For structural processors the timestep only depends on the speed of sound, c, and the smallest element dimension, L.In an Eulerian element however, the stress wave crosses