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Brief Description of Solution Techniques

Introduction
Computational technique in civil engineering is a powerful tool for finding approximate solution of engineering problems. Application ranges from deformation and stress analysis of automotive, aircraft, building and bridge structures to field analysis of heat flux, fluid flow, magnetic flux, seepage and other flow problems. Thus in computation technique domain or continuum, defining a complete region is discretized into simple geometric shapes called finite element and governing relations are considered over these elements and expressed in terms of unknown values at element corner. An assembly process, considering both loading and constraints results in set of equations. Solutions of these equations gives the approximate behavior of continuum.

Brief Description of Solution Technique
The formulation for structural analysis is based on three fundamental relations equilibrium, constitutive and compatibility. There are two major to analysis analytical and numerical technique.
Analytic approach leads to close solutions and is effective in case of simple geometry, boundary conditions, loading and material properties. However, in real as geometry may be complex as a result various numerical methods were arised. This method only give approximate solution to the problem and the suitability of method depends upon the processing power of computer and applicable to structure of arbitrary size and complexity.
The various method which are commonly used to solve solid and fluid mechanics problems are:

  1. Finite element method
  2. Finite difference method
  3. Boundary element method
  4. Discrete element method
  5. Smooth particle hydrodynamics

Finite element and finite difference method are discussed later on. Here, boundary element method is that we can approximate the solution of partial differential equation by looking at the solution of PDE on the boundary. BEM is useful on very large domain, where a FEM approximation would have too many elements to be practical.

 


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