# Intro by Jim Kennedy

### Thin Shell Plate

A simply supported plate of equal side length is subjected to a normal pressure on the top face. Differences between Belytschko-Tsai-Shell (elform 2), Hughes-Liu-Shell (elform 6) and fully integrated Shell (elform 16) can be studied. Example 1 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Thick Shell Plate

A simply supported plate of equal side length is subjected to a normal pressure on the top face. Differences between thick shell formulations (elform 2, 3 and 5) can be studied. Example 2 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Elliptical Thick Plate (coarse mesh)

An elliptical thick plate is subjected to a normal pressure on the top face. Differences between constant stress solid (elform 1), fully integrated S/R solid (elforms 2 and -1) and 8 point enhanced strain solid (elform 18) can be studied. Example 3 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Elliptical Thick Plate (fine mesh)

An elliptical thick plate is subjected to a normal pressure on the top face. Differences between constant stress solid (elform 1), fully integrated S/R solid (elforms 2 and -1) and 8 point enhanced strain solid (elform 18) can be studied. Example 4 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Snap-Back under Displacement Control

The implicit arc length method is used to solve the snap-back of the system. Differences between truss (elform 3) and discrete beam/cable (elform 6) can be studied. Example 5 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Straight Cantilever Beam

Analysis of a cantilever beam loaded at one end with a quasi-axial load. The material is elastic. Example 6 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Lee's Frame buckling Problem

A framed structure deforming under a load applied on one node. The frame is pinned to ground at two nodes. Arc-length method is used to capture the post-buckling behavior of the structure. Example 7 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Double Cross In-Plane Vibration

Behavior of beam elements in a modal analysis. The problem requires the extraction of numerically close eigenvalues. Differences between Hughes-Liu beam (elform 1), Belytschko-Schwer beam (elform 2) and linear Timoshenko beam (elform 13) can be studied. Example 8 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Thin Annular Plate (coarse mesh)

A simply supported annular plate is analyzed to determine the first natural frequencies. Example 9 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Thin Annular Plate (fine mesh)

A simply supported annular plate is analyzed to determine the first natural frequencies. Example 10 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Transient Response to Constant Force

A mass is attached in the middle of a beam. The beam is subjected to dynamic load. Example 11 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Square Plate Out-of-Plane Vibration (solid mesh)

Natural frequencies of a solid simply supported plate are determined. Differences between constant stress solid (elform 1), fully integrated S/R solid (elforms 2, -1 and -2) and fully integrated quadratic 8 node element with nodal rotations (elform 3) can be studied. Example 12 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Square Plate Out-of-Plane Vibration (thick shell mesh)

Natural frequencies of a solid simply supported plate are determined. Differences between S/R IPI thick shell (elform 2), assumed strain IPI thick shell (elform 3) and assumed strain RI thick shell (elform 5) can be studied. Example 13 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Square Plate Transient Forced Vibration (solid mesh)

Transient analysis is perfomed to obtain the response of a plate subjected to a suddenly applied pressure on its top. Differences between constant stress solid (elform 1), fully integrated S/R solid (elforms 2, -1 and -2) and fully integrated quadratic 8 node element with nodal rotations (elform 3) can be studied. Example 14 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Square Plate Transient Forced Vibration (thick shell mesh)

Transient analysis is perfomed to obtain the response of a plate subjected to a suddenly applied pressure on its top. Differences between S/R IPI thick shell (elform 2), assumed strain IPI thick shell (elform 3) and assumed strain RI thick shell (elform 5) can be studied. Example 15 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Transient Response of Cylindrical Disk

A cylindrical disk hits a deformable surface. Suitable contact algorithm is chosen. Example 16 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Linear Spring-Mass-System

A mass is attached to a linear spring. Period of vibration is determined. Example 17 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Nonlinear Spring-Mass-System

A mass is attached to a nonlinear spring. Period of vibration is determined. Example 18 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Thin Walled Cylinder Buckling

A cylinder is loaded with a uniformly distributed line load along the top edge. Critical buckling load is determined. Different meshes and differences between Belytschko-Tsay shell (elform 2), S/R Hughes-Liu shell (elform 6), Belytschko-Wong-Chiang shell (elform 10) and fully integrated shell (elform 16) can be studied.

### Membrane with Hot Spot

Analysis of the behavior of shell elements subjected to thermal load. Example 20 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### 1D Heat Transfer (Radiation)

A bar radiates to an ambient temperature at one end and to a constant temperature at the other end. Example 21 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### 1D Heat Transfer (Bar)

A bar is subjected at one end to a varying temperature and at the other end to a constant temperature. Example 22 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### 2D Heat Transfer (Convection)

A slab is subjected to thermal loads for a steady state simulation. Example 23 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### 3D Thermal Load

A solid cylinder is subjected to a prescribed temperature gradient. Different meshes can be studied. Example 24 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Cooling via Radiation

A billet looses heat by radiation from all its surfaces to its surroundings. Example 25 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Pipe Whip

This problem illustrates a high speed, large deformation event with contact. Example 26 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### Bar Impacting a Rigid Wall

A deformable copper bar impacts a rigid wall at high speed. Differences in contact modelling via *RIGIDWALL_PLANAR and *CONTACT_AUTOMATIC_SURFACE_TO_SURFACE can be studied. Solutions with constant stress solid (elform 1), fully integrated S/R solid (elforms 1, -1, -2), 1 point tetrahedron (elform 10), 1 point nodal pressure tetrahedron (elform 13) and 1 point ALE (elform 5) can be studied. Example 27 from Introductory Manual for LS-DYNA Users by James M. Kennedy.

### The Examples Manual

This guide is mainly addressed to first-time users. Several of the problems present a closed-form solution, while others a reference solution obtained by using an arbitrary refined mesh (NAFEMS Benchmarks). Most of the problems are IMPLICIT ones.