Single-Course Dansk 5 ECTS

Numerical Methods in Structural Mechanics

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Overall Course Objectives

To enable the participants to understand and apply computational models for statically determinate and indeterminate elastic beam, frame, membrane and plated structures, including discretization of continuous models for finite element analysis. Furthermore, to make the participants able to operate a commercial Finite Element Method program for analysis of plane and spatial structures.

See course description in Danish

Apply the Deformation/Stiffness Method to solve simple beam, truss and frame problems by hand calculations.
Explain the assemblage of the global stiffness matrix and load vector for plane trusses and frames including accounting for boundary conditions.
Explain the equivalence between the Deformation/Stiffness Method and the Finite Element Method.
Use a mathematics program to analyze statically indeterminent truss and frame structures using the Deformation/Stiffness method.
Account for the interpolation functions for simple bar, beam and plane elements.
Account for the transformation of element stiffness matrices.
Account for the solution of the global finite element system.
Use a commercial finite element program to solve truss, frame, membrane and plate problems.
Perform convergence analysis for a finite element analyses.
Analyze and evaluate deformations and stress distributions in a commercial finite element program.
Critically evaluate the importance of the choice of element types, size and boundary conditions in finite element analysis.
Perform finite element analysis of selected applied structural design problems.

The course concerns statically indeterminate elastic structures and analysis methods such as the Deformation/Stiffness Method and the Finite Element Method for plane and spatial structures, as well as application and training in the use of a commercial Finite Element Method (FEM) program within the civil engineering and naval architecture fields.

The course has the following content:
– The Deformation/Stiffness method for trusses and frames.
– Distributed loads and equivalent nodal loads for bars and beams.
– Element stiffness matrix for plane beam elements, 2D and 3D beam elements.
– Transformation of elements in the plane.
– Boundary conditions and symmetry conditions.
– The Finite Element Method (FEM)
– Basic plane and solid continuum element types (formulations, advantages and disadvantages).
– Iso-parametric plane and spatial elements.
– Equivalent nodal loads for plane and solid continuum elements.
– Gaussian integration.
– Stress determination and mesh distribution.