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Analytical Methods

Lollipop

The application is intended for linear static and dynamic analysis of beam structures using the Finite Element Method. It is general purpose in scope and easy to use. Solution of small to moderate size problems can be obtained.

For static analyses, displacements throughout the structure are found along with forces and moments in each beam element. For dynamic analyses, natural frequencies, mode shapes, generalized masses, modal masses, and base motion participation factors are obtained along with normalized forces and moments in each beam element. Both displacements and mode shapes can be plotted or animated. Forces and moments can be contoured.

Beam-2D was developed for use by design engineers, civil, structural, and mechanical engineering students, and experienced professionals who desire rapid and accurate solutions to a wide variety of problems.

The modeling and analysis process consists of the following steps:
1: Name the model
2: Select system of units
3: Define coordinate system (optional):
- Cartesian or polar
- x-y coordinates of origin
4: Add materials:
- material name
- modulus of elasticity E
- weight density rho
- coefficient of thermal expansion CTE
5: Add sections:
- section name
- moment of inertia
- crossectional area
6: Add nodes:
- x coordinate
- y coordinate
7: Add beam elements:
- end I node
- end J node
- material
- section properties
- delta temperature
8: Add forces and moments to nodes:
- node for application of load
- load magnitude
- load direction x-y-z
9: Add masses to nodes (optional):
- node for application of mass
- mass magnitude
10: Add boundary springs to nodes (optional):
- node for application of spring
- spring rate (force/displacement)
- or spring rate (moment/angle)
- spring direction x-y-z
11: Add restraints to nodes:
- node to restrain
- x displacement restraint
- y displacement restraint
- z rotation restraint
12: Solve the system of linear equations:
- displacements for static
- frequencies and mode shapes for dynamic
13: View results
- view text file
- share text file
- plot displacements or mode shapes
- animate displacements or mode shapes
- plot forces
- plot stresses


Beam-2D

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