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These included elasticity theory, energy principles in structural mechanics, flexibility method and matrix stiffness method. It was through analysis of these methods that the direct stiffness method emerged as an efficient method ideally suited for computer implementation.
The origin of finite method can be traced to the matrix analysis of structures [1] [2] where the concept of a displacement or stiffness matrix approach was introduced. Finite element concepts were developed based on engineering methods in 1950s.
Commercial computer software for structural analysis typically uses matrix finite-element analysis, which can be further classified into two main approaches: the displacement or stiffness method and the force or flexibility method. The stiffness method is the most popular by far thanks to its ease of implementation as well as of formulation for ...
Generally, FEM is the method of choice in all types of analysis in structural mechanics (i.e., solving for deformation and stresses in solid bodies or dynamics of structures). In contrast, computational fluid dynamics (CFD) tend to use FDM or other methods like finite volume method (FVM).
The matrix method is a structural analysis method used as a fundamental principle in many applications in civil engineering. The method is carried out, using either a ...
In structural engineering, the flexibility method, also called the method of consistent deformations, is the traditional method for computing member forces and displacements in structural systems. Its modern version formulated in terms of the members' flexibility matrices also has the name the matrix force method due to its use of member forces ...
The goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration.It is common to use the finite element method (FEM) to perform this analysis because, like other calculations using the FEM, the object being analyzed can have arbitrary shape and the results of the calculations are acceptable.
Plasticity theory can be used for some reinforced concrete structures assuming they are underreinforced, meaning that the steel reinforcement fails before the concrete does. Plasticity theory states that the point at which a structure collapses (reaches yield) lies between an upper and a lower bound on the load, defined as follows: