# BEAMUP

### Overview

The program BEAMUP described below is being developed to automate stress analysis for two-dimensional problems. The user would describe the geometry, material properties, loading, and the desired accuracy. The appropriate mesh would be created within the program and the user would not need to know boundary element method on which the program is based. Details of the automation can be found in my paper "Controlling errors in the process of automating boundary element method analysis" EABE v26, pp405-415,(2002).

BEAMUP is a general purpose two-dimensional computer program based on the boundary element method that can be used for solving a vast variety of problems in engineering. The boundary element method offers significant computational advantages over other numerical methods for four class of problems:

#### Problems in which the boundary is changing such as in shape optimization and crack growth. Problems in which the shape is complex such as grain boundary, geological flaws, and threads of a screw. Problems in which large gradients are present such as the gradients in stresses or heat near cracks, re-entrant corners, inclusions, dislocations and material interfaces. Problems in which the domain is infinite such as in the calculations of stress in the earth around mines, tunnels, rail beds, highways, and faults in earth.

The above described problems can be solved using the four boundary value problems listed below.

• Elastostatic
• Fracture Mechanics
• Poisson's Equation (Under Construction)
• Plate Bending (Under Construction)

The description below is applicable to the four types of boundary value problems described above and presupposes some knowledge of the boundary element method.

The solution technique can be the Direct BEM or the Indirect BEM. Body can be made of single or multiple materials . Material can be isotropic or orthotropic for elastostatic and Poisson's problems. Point singularities (e.g. concentrated force or moment), line singularities (e.g. line loads in the interior), and distributed singularities (body force) can be modelled.The interpolation function for each element can be a polynomial of order 6 or less and satisfy any order of continuity between elements. As described in the pages of individual applications several types of singularities can be used in the indirect formulations. User could also write a subroutine to describe the influence function with any integer order of singularity.Boundary conditions are specified in the local normal and tangential coordinate system. Boundary conditions could be on primary variable, secondary variables, mixed and several combinations of primary and secondary varriables(e.g. spring, friction etc.) Click on one of the above four applications to get detail information on each topic.