Course detail

Structural mechanics

FAST-DD51Acad. year: 2021/2022

Advance topics on FEA. Introduction to nonlinear mechanics. Tensors, strain and stress measures, coordinate systems, solution methods tangent stiffness matrix, material and geometrical stiffness, unbalanced forces. Linear and nonlinear buckling post critical analysis, mechanisms, cables, membranes. Modelling of the structure-soil interaction.

Language of instruction

Czech

Guarantor

doc. Ing. Vlastislav Salajka, CSc.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

Not applicable.

Prerequisites

Basic knowledge of structure mechanics, matrix and vector algebra, infinitesimal calculus, fundamentals of numerical mathematics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1.Variational principles in the mechanics of bodies.
Lagrangian and Castiglian variational principles,
more general variational principles.
2.Finite element method.
Continuity on the boundaries,
convergence criteria, various kinds of elements.
3.Fundamentals of nonlinear mechanics
Strain and stress measures, total Lagrangian and updated Lagrangian methods
4.Numerical solution of nonlinear problems.
Newton-Raphson procedure and its modifications,
deformation control, arc length.
5.Tangent stiffness matrix.
Material stiffness matrix, stress stiffness matrix,
influence of nonlinear members of the strain tensor.
6.Evaluation of unbalanced nodal forces
Criteria for ending of iterations
7.Linear and nonlinear stability
8.Post critical analysis of structures
9.Analysis of mechanisms, cables, membranes
10.Energetical definition of surface subsoil model
11.Reduction of dimension and area of the structure-soil interaction model
12.Subsoil model introduced by the Czech code,
calculation of stress by the theory of elastic half space,
structure settlement.
13. Foundation plates on piles

Work placements

Not applicable.

Aims

Lectures are oriented to post gradual students with aim to make their knowledge in structure mechanics deeper. The topics are selected from the point of view of their application in advance structure analysis.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

doc. Ing. Vlastislav Salajka, CSc.

Syllabus

1.Variational principles in the mechanics of bodies. Lagrangian and Castiglian variational principles, more general variational principles. 2.Finite element method. Continuity on the boundaries, convergence criteria, various kinds of elements. 3.Fundamentals of nonlinear mechanics Strain and stress measures, total Lagrangian and updated Lagrangian methods 4.Numerical solution of nonlinear problems. Newton-Raphson procedure and its modifications, deformation control, arc length. 5.Tangent stiffness matrix. Material stiffness matrix, stress stiffness matrix, influence of nonlinear members of the strain tensor. 6.Evaluation of unbalanced nodal forces Criteria for ending of iterations 7.Linear and nonlinear stability 8.Post critical analysis of structures 9.Analysis of mechanisms, cables, membranes 10.Energetical definition of surface subsoil model 11.Reduction of dimension and area of the structure-soil interaction model 12.Subsoil model introduced by the Czech code, calculation of stress by the theory of elastic half space, structure settlement. 13. Foundation plates on piles