Course detail

# Structural Mechanics

FAST-BD006Acad. year: 2018/2019

Mathematical models and FEM, basic assumptions, linear 3D models, constitutive relations, design models for solving engineering problems (planar beam task models, bent plates, shells, tasks of heat flow), process solutions, variant of formulation of FEM, discretization, derivation matrix stiffness of the 2D element, equilibrium equations. Isoparametric elements, numerical integration to calculate the stiffness matrix and load vector elements for solving various problems, generation FE mesh and the influence on the accuracy of the solution, singularity, the possibility of nonlinear problems solving and problems of FEM stability, software based on FEM.

Supervisor

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

After completing the course the student will know the basics of finite element method (FEM), which practically utilized. Become familiar with mathematical models of structures for solving engineering problems. He/she will know the principle of the assembly of the stiffness matrix and load vector finite element (FE) and subsequent assembly of the equilibrium equations of the structure. Understand the essence of isoparametric elements. Student can discretize the design and choose the appropriate type of FE for selected solutions. He/she will know about the possibilities of solving nonlinear FEM tasks and can use the knowledge for solving structural stability.

Prerequisites

Static analysis of statically determinate and indeterminate planar beam structures with straight and curved centreline; calculation of deformations via unit forces method; force method; influence support relaxation and the influence of temperature changes; theory of strength and failure; stress and strain in point of the solid, the principal stresses.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Methods of teaching are lectures and exercises. Individual consultations complement teaching. Study activities of student include entering his own independent work. Attendance at lectures is recommended. Participation in other classes is required and controlled.

Assesment methods and criteria linked to learning outcomes

The subject is completed by credit and final examination. For credit the student should pass all written tests in selected exercises. The credit is the necessary condition for final examination entrance. The final examination consists of written and oral parts. The written examination part includes both examples and theory. The positive result in written examination allows the student to pass to oral part.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

1. Introduction to the Finite Element Method (FEM) of solids and structures. Mathematical models and FEM. Detail of models. The basic assumptions for solving problems of mechanics of structures.

2. Solution of beam structures. Linear 3D mathematical models. Deformation. Stress. Constitutive equations. Formulation of linear / non-linear tasks.

3. Mathematical models of structures for solving engineering problems (2D beam models, bent plates, shells, tasks of heat flow, other force fields). The principle of virtual work.

4. Procedure FEM. Formulation of 1D and 2D tasks. Discretization. Equilibrium equation.

5. Isoparametric elements. Basic considerations. Stiffness matrix and load vector of 1D and 2D element. Numerical integration to calculate the stiffness matrix and load vectors.

6. The finite elements (FE) for beams, plates and shells.

7. FEM modelling of structures. The combination of elements. Boundary conditions. Rigid connections. Spring. Singularity.

8. Generation of FE mesh. Check-shaped elements and softness meshes. The accuracy of the solution.

9. Potential solutions of nonlinear problems via FEM. Geometric, material nonlinearity and contact.

10. Identification of a critical load of the structure. Matrix notation of stability task in FEM and its solution.

11. Software for solving FEM. Pre-processor, solver and post-processors.

Aims

Introduction to the structural analysis of solution of plane trusses of loading mobile load. Evaluation of the influence lines and determination of its extremes.

Structures with bars of varying cross-section. Elastic and eccentric connection of bars within the frame structures. The analysis of linear stability of the frame structures, Euler’s critical force and the shapes of buckled structure.

The principle of solution of the thin-walled bars with opened cross-section, equation of restrained warping torsion of opened cross-section shape.

Introduction to the elasto-plastic analysis of a bar. The plastic limit load carrying capacity of a frame structure. The limit failure states.

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.

Classification of course in study plans

- Programme B-P-C-SI (N) Bachelor's
branch K , 4. year of study, summer semester, 5 credits, compulsory

- Programme B-P-E-SI (N) Bachelor's
branch K , 4. year of study, summer semester, 5 credits, compulsory

- Programme B-K-C-SI (N) Bachelor's
branch K , 4. year of study, summer semester, 5 credits, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

1. Introduction to the Finite Element Method (FEM) of solids and structures. Mathematical models and FEM. Detail of models. The basic assumptions for solving problems of mechanics of structures.

2. Solution of beam structures. Linear 3D mathematical models. Deformation. Stress. Constitutive equations. Formulation of linear / non-linear tasks.

3. Mathematical models of structures for solving engineering problems (2D beam models, bent plates, shells, tasks of heat flow, other force fields). The principle of virtual work.

4. Procedure FEM. Formulation of 1D and 2D tasks. Discretization. Equilibrium equation.

5. Isoparametric elements. Basic considerations. Stiffness matrix and load vector of 1D and 2D element. Numerical integration to calculate the stiffness matrix and load vectors.

6. The finite elements (FE) for beams, plates and shells.

7. FEM modelling of structures. The combination of elements. Boundary conditions. Rigid connections. Spring. Singularity.

8. Generation of FE mesh. Check-shaped elements and softness meshes. The accuracy of the solution.

9. Potential solutions of nonlinear problems via FEM. Geometric, material nonlinearity and contact.

10. Identification of a critical load of the structure. Matrix notation of stability task in FEM and its solution.

11. Software for solving FEM. Pre-processor, solver and post-processors.

Exercise

26 hours, compulsory

Teacher / Lecturer

Syllabus

1. Solving simple discrete problems of elasticity.

2. Analysis of the derivation of the element stiffness matrix for plane stress. Calculating deformations of simple wall.

3. Calculation of the matrix of elasticity constants of the different types of elements.

4. Analysis algorithm assembly stiffness matrix and load vector of the different types of elements. Approximate functions for various types of elements.

5. Stating stiffness matrix of isoparametric element.

6. Numerical integration – application examples. Entering the boundary conditions. Singularity and stress concentration.

7. Derivation of finite element of plates and shells.

8. Modelling of simple tasks of FEM. The combination of elements. Boundary conditions. Rigid connections. Spring. Joining elements.

9. Application software for solving stability – model creation.

10. Calculation of critical load and analysis of the results.

11. Analysis of modelling structures process. Definition of input data and selection of types of finite elements. Credit.