## Theory of Elasticity and Plasticity

Major Structural Engineering - in English Faculty of Structural Engineering Structural Mechanics Assoc. Prof. Dr. Eng. Dobromir Dinev

Year of education: III, Semester: 6, summer
Assessment: exam
Method of teaching: lectures and seminars
Total hours: 30 lectures and 30 seminars (Academic Hours)
ECTS credits 4

Goals and objectives of the subject:
The goal of the subject is to consolidate the structural mechanics principles, presented in the previous years of study and to equip the students with skills required to solve a range of engineering problems they not seen before. Students will gain a deep understanding of the concepts and methods underlying modern theory of elasticity and plasticity.
Characteristics of the subject: This course teaches the fundamentals for the analysis of structures in engineering with a specific focus on two-dimensional and three-dimensional structures. The subject can be regarded as an advanced part of the Strength of materials class.
The lectures are split into two modules: theory of elasticity and theory of plasticity. The theory of elasticity module covers general mathematical theory of analysis of stress, strain and deformation of a solid body. The module continues with a constitutive modelling of the different type of linear-elastic materials. This part ends with a description of the boundary conditions, elasticity fundamental problem formulation with general solution strategies. The basics of the energy principles are described with an emphasis on the minimum potential energy principle and application of the Ritz method. The applied elasticity part is focused on the specific topics which include plane stress and plane strain state formulated by the Airy stress function with application of the polynomial solution; plate analysis with application of the classical plate theory, analytical, numerical, and engineering solutions of the problem; the shell analysis covers a general membrane and bending theories and solution of shells of revolution under an axi-symmetric loading.
The basic principles of the plasticity are presented into the second module. An elastic-perfectly plastic material model is a basis of the solution strategy. The analysis part of the module starts with a concentrated plasticity and plastic hinges applied on the plastic collapse analysis of beams. The lower-bound and upper-bound solutions are presented. Later these solutions are applied on the plastic analysis of slabs (yield-line and strip methods). The module finishes with an analysis and design of discontinuity regions by application of the “strut-and-tie” modelling.
Acquired knowledge:

• An advanced understanding of the linear-elastic and plastic behaviour of solids and structures
• Explain the theory, concepts, principles of solid mechanics
• Derive the governing equations for 3D and 2D elastic problems
• Solve these problems with various solution technics
• Understand contemporary issues in solid mechanics research

Acquired skills:

• Model an engineering structure without detailed instructions
• Critical thinking and judgement of the adopted assumptions and results of the solutions
• Interpretation and analysis of data
• Ability to undertake problem identification, formulation, and solution
• Apply the theory to problems of practical interest
• Ability to apply knowledge of science and engineering fundamentals
• Develop skills in collaborative learning through small-group problem solving and communication

Preliminary requirements: Strength of materials

#### Study materials

ТЕ9 Elasticity theory - schemes
Prof. Dr. Eng. Georgi Todorov