Finite Element Analysis in Geotechnical Engineering
Expert-defined terms from the Postgraduate Certificate in Geotechnical Engineering & Soil Mechanics course at London School of Planning and Management. Free to read, free to share, paired with a globally recognised certification pathway.
Finite Element Analysis (FEA) #
A numerical method used to solve partial differential equations that describe problems in engineering and physics. It involves dividing a complex domain into smaller, simpler elements and solving the equations of equilibrium for each element. The results are then assembled to obtain the solution for the entire domain.
Geotechnical Engineering #
A branch of civil engineering concerned with the behavior of soils and rocks and their interaction with structures. It involves the study of soil mechanics, rock mechanics, and engineering geology.
Soil Mechanics #
A branch of geotechnical engineering that deals with the behavior of soils under external loads, such as those imposed by foundations, embankments, and retaining walls. It involves the study of soil properties, such as strength, stiffness, and permeability, and the application of these properties to the design of geotechnical structures.
Finite Element Method (FEM) #
A numerical technique used in FEA to approximate the solution of partial differential equations. It involves dividing the domain into a set of discrete elements and solving the equations of equilibrium for each element. The results are then assembled to obtain the solution for the entire domain.
Element #
A small, discrete portion of the domain that is used in FEA to approximate the solution of partial differential equations. Elements can be one-, two-, or three-dimensional and can take various shapes, such as triangles, quadrilaterals, and hexahedra.
Node #
A point in the finite element mesh where the displacements or other variables are calculated. Nodes are typically located at the corners of elements and are connected by element edges or faces.
Degree of Freedom (DOF) #
The number of independent displacement components at a node. For example, a node in a two-dimensional problem has two degrees of freedom, one in the x-direction and one in the y-direction.
Displacement #
The vector of displacements at all nodes in the finite element mesh. Displacements are the primary unknowns in FEA and are used to calculate the strains and stresses in the elements.
Strain #
A measure of the deformation of an element in response to applied loads. Strains are calculated from the displacements and are used to compute the stresses in the elements.
Stress #
A measure of the internal forces in an element. Stresses are calculated from the strains and are used to evaluate the safety and performance of the geotechnical structure.
Boundary Conditions #
The prescribed values of displacements or forces at the boundaries of the domain. Boundary conditions are used to specify the external loads and constraints on the geotechnical structure.
Initial Conditions #
The prescribed values of displacements or velocities at the beginning of the analysis. Initial conditions are used to simulate the initial state of the geotechnical structure.
Material Properties #
The values of material parameters, such as elastic modulus, Poisson's ratio, and density, that describe the behavior of the soil or rock. Material properties are used to calculate the strains and stresses in the elements.
Mesh Generation #
The process of creating the finite element mesh by dividing the domain into smaller elements. Mesh generation involves selecting the element type, shape, and size, and locating the nodes and boundaries.
Convergence #
The process of refining the mesh until the solution converges to a stable value. Convergence is achieved by reducing the element size and increasing the number of elements.
Nonlinear Analysis #
A type of FEA that considers the nonlinear behavior of the soil or rock, such as plasticity, large strains, and material nonlinearity. Nonlinear analysis is used to simulate the complex behavior of geotechnical structures under extreme loads or long-term deformations.
Sensitivity Analysis #
A type of FEA that evaluates the effect of changes in material properties or boundary conditions on the solution. Sensitivity analysis is used