Introduction to Explicit Dynamics

Welcome to the ANSYS Explicit Dynamics introductory training course!

This training course is intended for all new or occasional ANSYS Explicit Dynamics users, regardless of the CAD software used.

Course Objectives:

-Introduction to Explicit Dynamics Analyses.

-General understanding of the Workbench and Explicit Dynamics (Mechanical) user interface, as related to geometry import and meshing.

-Detailed understanding of how to set up, solve and post-process Explicit Dynamic analyses.

-Utilizing parameters for optimization studies.

Training Courses are also available covering the detailed use of other Workbench modules (e.g. DesignModeler, Meshing, Advanced meshing, etc.).

Course Materials

-The Training Manual you have is an exact copy of the slides.

-Workshop descriptions and instructions are included in the Workshop Supplement.

-Copies of the workshop files are available on the ANSYS Customer Portal (www.ansys.com).

-Advanced training courses are available on specific topics. Schedule available on the ANSYS web page http://www.ansys.com/ under “Solutions> Services and Support> Training Services”.

Why Use Explicit Dynamics?

“Implicit” and “Explicit” refer to two types of time integration methods used to perform dynamic simulations

Explicit time integration is more accurate and efficient for simulations involving

-Shock wave propagation

-Large deformations and strains

-Non-linear material behavior

-Complex contact

-Fragmentation

-Non-linear buckling

Typical applications

-Drop tests

-Impact and Penetration

Impact Response of Materials

Typical Values for Solid Impacts

Aerospace Applications

Applications in Nuclear Power safety

Sporting Goods Application

Explicit Solution Strategy

-Solution starts with a mesh having assigned material properties, loads, constraints and initial conditions.

-Integration in time, produces motion at the mesh nodes

-Motion of the nodes produces deformation of the elements

-Element deformation results in a change in volume and density of the material in each element

-Deformation rate is used to derive strain rates (using various element formulations)

-Constitutive laws derive resultant stresses from strain rates

-Stresses are transformed back into nodal forces (using various element formulations)

-External nodal forces are computed from boundary conditions, loads and contact

-Total nodal forces are divided by nodal mass to produce nodal accelerations

-Accelerations are integrated Explicitly in time to produce new nodal velocities

-Nodal velocities are integrated Explicitly in time to produce new nodal positions

-The solution process (Cycle) is repeated until the calculation end time is reached

Basic Formulation–Implicit Dynamics

The basic equation of motion solved by an implicit transient dynamic analysis is

where m is the mass matrix, c is the damping matrix, k is the stiffness matrix

and F(t) is the load vector

At any given time, t, this equation can be thought of as a set of "static" equilibrium equations that also take into account inertia forces and damping forces. The Newmark or HHT method is used to solve these equations at discrete time points. The time increment between successive time points is called the integration time step

For linear problems:

-Implicit time integration is unconditionally stable for certain integration parameters.

-The time step will vary only to satisfy accuracy requirements.

For nonlinear problems:

-The solution is obtained using a series of linear approximations (Newton-Raphson method), so each time step may have many equilibrium iterations.

-The solution requires inversion of the nonlinear dynamic equivalent stiffness matrix.

-Small, iterative time steps may be required to achieve convergence.

-Convergence tools are provided, but convergence is not guaranteed for highly nonlinear problems.

The basic equations solved by an Explicit Dynamic analysis express the conservation of mass, momentum and energy in Lagrange coordinates. These, together with a material model and a set of initial and boundary conditions, define the complete solution of the problem.

For Lagrange formulations, the mesh moves and distorts with the material it models, so conservation of mass is automatically satisfied. The density at any time can be determined from the current volume of the zone and its initial mass:

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