Finite Element Method in Structural Mechanics

Major: Industrial and Civil Construction
Code of subject: 7.192.01.O.003
Credits: 3.00
Department: Bridges and Structural Mechanics
Lecturer: Ihor Butrynskyi, assoc. prof.б Ph.D.
Semester: 1 семестр
Mode of study: денна
Мета вивчення дисципліни: To provide knowledge that will allow to apply the method of finite elements for the calculation of structures, to model the behavior of the elements of structures and the behavior of structures as a whole.
Завдання: The study of an educational discipline (OK2.2) involves the formation and development of the following competencies in students of education (numbering according to the OPP): Integral (INT) INT. The ability to solve complex engineering-technical and scientific-applied problems during research and professional activities in the field of construction and civil engineering and in the learning process using modern information and innovative technologies. General (ZK): ZK 1. Ability to abstract thinking, analysis and synthesis. ZK 2. Ability to conduct research at an appropriate level. ZK 4. Ability to make informed decisions. Special professionals (SK): SK05. The ability to carry out surveys, tests, diagnostics and calculations when solving complex problems of a research and innovation nature in the field of construction and civil engineering. SK 06. Ability to build and investigate models of situations, objects and processes of construction and civil engineering SK 07. Ability to use specialized computer programs when solving complex engineering problems in the field of construction and civil engineering. Special professional competences of a professional direction (SKP) SCP 1.2. The ability to develop specialized sections of project documentation, monitor implementation during the construction and operation of industrial and civil buildings
Learning outcomes: As a result of studying the academic discipline (OK 2.2) and completing the course work (OK 2.7), the applicant must be able to demonstrate the following learning outcomes: know: principles, relationships, algorithms, features of using the finite element method in solving problems of the mechanics of structures, in particular: - fundamentals of finite element modeling; - basic formulations of finite elements - relations in matrix form and algorithms of finite element methods for problems of statics, stability and dynamics of buildings; - methods of assessing the accuracy of solving problems using the finite element method; be able: - to formulate, analyze and solve the problems of the mechanics of structures using the finite element method, in particular: - develop finite element models of building elements; - formulate relations that describe Hermitian and Lagrangian finite elements; - calculate stiffness matrices, masses, load vectors of finite elements and the system as a whole; - apply the MSE algorithm to obtain a numerical solution to problems of statics, stability and dynamics of rod systems; - to analyze the results obtained with the use of TSE, to evaluate the accuracy of the numerical solution. Program learning outcomes of the educational discipline OK 2.2 RN 01. Design common industrial and civil buildings and structures, including using computer design software systems. RN 06. Apply modern mathematical and numerical methods for analysis, calculation and optimization of design parameters of industrial and civil buildings and structures. RNS 1.1. Apply the acquired knowledge and understanding to identify, formulate and solve the design, construction and operation of industrial and civil objects. ЗН1. Specialized conceptual knowledge that includes current scientific achievements in the field of professional activity or field of knowledge and is the basis for original thinking and conducting research Program learning results of coursework in the educational discipline OK 2.7 RN 01. Design common industrial and civil buildings and structures, including using computer design software systems. RN 06. Apply modern mathematical and numerical methods for analysis, calculation and optimization of design parameters of industrial and civil buildings and structures. RNS 1.1. Apply the acquired knowledge and understanding to identify, formulate and solve the design, construction and operation of industrial and civil objects. UM2. Ability to integrate knowledge and solve complex problems in broad or multidisciplinary contexts.
Required prior and related subjects: • Mathematical analysis; • Theoretical mechanics; • Strength of Materials; • Structural mechanics; • Stability and Dynamics of Structures
Summary of the subject: Formulation of variational-difference methods for calculating discrete models of buildings. Formulation of finite elements. Finite element and approximation. Finite element model. FEM in displacements for structural statics problems. Stiffness matrix of rod elements and load vector. Transformations of coordinates. Assembling. Boundary conditions. Equations and finite elements of the plane problem of the theory of elasticity, plates and shells. FEA for the spatial problem of the theory of elasticity. Convergence and estimation of the accuracy of the finite element approximation. Formulation of problems of dynamics in FEM. Mass matrix. FEA for structural dynamics. Geometric stiffness matrix. FEA for geometrically and physically nonlinear problems. The course work involves the implementation of the FEM computational algorithm for a model problem and the FEA using FEM-FEA software.
Опис: Basis. Boundary problem formulation, variational formulation of boundary problems. Approximate methods, convergence and stability of approximate method. Basic variational-difference methods for structural analysis: grid, finite element (FEM), boundary element methods. Direct, Galerkin-Ritz method, variational formulation of FEM. FEM for beams and frames. Structures discretization, finite element. Euler-Bernoulli bar-beam element. Interpolation, approximation and shape function. Stiffness matrices and equivalent loads vectors, transformation matrix. Assembling; basic algorithms for solving equations. Timoshenko FE beam element. Nonlinear FEM analysis of beams and frames. Geometric and material nonlinearities. Geometric, incremental, initial stress stiffness matrix. Linear and nonlinear buckling analysis. Plastic hinge analysis. Solving of nonlinear equations systems: incremental, iterative and mixed procedures, Newton-Raphson, arc-length method. FEM for dynamic analysis. Mass and damping matrix, Rayleigh damping. Free vibration, harmonic forced vibration. Time response analysis: modal superposition and direct time integration methods. FEM for 2D problems. The plane elasticity problems. 2-D elements: formulation, approximation. 3-node triangular, 4-node quadrilateral. Isoparametric formulation, the Jacobian matrix, numerical integration. Higher order elements. Reduced integration. Plate bending and shell elements. FEM modeling techniques: choice of elements, meshing, matching and non-matching meshes; connections, supports and loads modeling, checking and solution error estimating. The course work thems: FEA of frame for static load. FEA of frame with geometrically-nonlinear elements. FEA of frame with material-nonlinear elements. FEA of frame backling. Geometrically-nonlinear FEA of frame. Free vibration analysis of frame using FEM. Harmonic forced vibration analysis of frame using FEM. Time response analysis of frame for complex law of excitation. Time response analysis of frame for seismic excitation. FEA of two-dimensional stress-strain state of the plate. FEA of stress state for thin plate bending.
Assessment methods and criteria: Theoretical course: current control (work and surveys at lectures and classes, solving problems ) - 40 %; exam - 60%. Coutse work: progress - 50%, CW defencing - 50%
Критерії оцінювання результатів навчання: Current control: surveys and knowledge level testing. Exam. Course work: percentage of progress, quality control. Defense of the CW: assessment abilities of solving practical structural problems using FEA. Criteria - see subsection "Procedure and criteria for issuing grades"
Порядок та критерії виставляння балів та оцінок: 88-100 points - ("excellent") - an excellent level of theoretical knowledge and practical skills (perfect mastery of lecture material and additional recommended literary sources, the ability to analyze phenomena in their relationship and development, correctly, succinctly, logically, consistently answer asked questions, the ability to effectively apply knowledge and skills to solve typical and atypical new problems); 71-87 points - ("good") - a good level of theoretical knowledge and practical skills (perfect mastery of lecture material, ability to analyze phenomena, correctly answer questions, ability to solve typical practical problems); 70 – 50 points – (“satisfactory”) satisfactory level of theoretical knowledge and practical skills (partial mastery of lecture material at the level of more than 50%, ability to classify phenomena, correctly answer questions, ability to solve considered basic problems); 26-49 points - ("not certified" with the possibility of repeating the semester control) - unsatisfactory knowledge - ignorance of a large part of the educational material, fundamental errors in answers to basic questions, inability to apply theoretical provisions when solving practical typical problems, errors classification of problems in solving typical problems; 00–25 points – (“unsatisfactory” with mandatory re-study) ignorance of most of the educational material, ignorance of the basic fundamental principles and theoretical provisions in answering questions, inability to navigate when solving practical problems, fundamental and essential errors in the classification of problems when solving typical problems
Recommended books: 1. Баженов В.А., Перельмутер А.В., Шишов О.В. Будівельна механіка. Комп’ютерні технології і моделювання: підручник. – К.: ПАТ “ВІПОЛ”, 2013. – 896 с. 2. Баженов В.А., Перельмутер А.В., Шишов О.В. Будівельна механіка. Комп’ютерні технології: підручник. – К.: Каравела, 2009. – 696 с. 3. Дубенець В.Г., Хільчевський В.В., Савченко О.В. Основи методу скінченних елементів: навчальний посібник. Чернігів: ЧДТУ, 2007. 287с. 4. Zienkiewicz, OC; Taylor, RL. The Finite Element Method for Solid and Structural Mechanics. 6-th ed, Elsevier Butterworth-Heinemann, 2005 . – 648p. 5. Wilson E. L. Three Dimensional Static and Dynamic Analysis of Structures. 3-rd Ed. CSI, 2002 – 423p 6. Rene De Borst, Mike A. Crisfield Nonlinear Finite Element Analysis of Solids and Structures, 2nd Ed, Wiley, 2012 – 540p.
Уніфікований додаток: Lviv Polytechnic National University ensures the realization of the right of persons with disabilities to obtain higher education. Inclusive educational services are provided by the Service of accessibility to learning opportunities "Without restrictions", the purpose of which is to provide permanent individual support for the educational process of students with disabilities and chronic diseases. An important tool for the implementation of the inclusive educational policy at the University is the Program for improving the qualifications of scientific and pedagogical workers and educational and support staff in the field of social inclusion and inclusive education. Contact at: St. Karpinsky, 2/4, 1st floor, room 112 E-mail: nolimits@lpnu.ua Websites: https://lpnu.ua/nolimits https://lpnu.ua/integration
Академічна доброчесність: The policy regarding the academic integrity of the participants of the educational process is formed on the basis of compliance with the principles of academic integrity, taking into account "Regulations on academic integrity at the Lviv Polytechnic National University" (approved by the academic council of the university on June 20, 2017, protocol No. 35).

Finite Element Method in Structural Mechanics (курсова робота)

Major: Industrial and Civil Construction
Code of subject: 7.192.01.O.007
Credits: 2.00
Department: Bridges and Structural Mechanics
Lecturer: Ihor Butrynskyi, assoc. prof.б Ph.D.
Semester: 1 семестр
Mode of study: денна
Мета вивчення дисципліни: To provide skils that will allow to apply the method of finite elements for the calculation of structures, to model the behavior of the elements of structures and the behavior of structures as a whole.
Завдання: The Course Work (OK2.7) involves the formation and development of the following competencies in students of education (numbering according to the OPP): Integral (INT) INT. The ability to solve complex engineering-technical and scientific-applied problems during research and professional activities in the field of construction and civil engineering and in the learning process using modern information and innovative technologies. General (ZK): ZK 1. Ability to abstract thinking, analysis and synthesis. ZK 2. Ability to conduct research at an appropriate level. ZK 4. Ability to make informed decisions. Special professionals (SK): SK05. The ability to carry out surveys, tests, diagnostics and calculations when solving complex problems of a research and innovation nature in the field of construction and civil engineering. SK 06. Ability to build and investigate models of situations, objects and processes of construction and civil engineering SK 07. Ability to use specialized computer programs when solving complex engineering problems in the field of construction and civil engineering. Special professional competences of a professional direction (SKP) SCP 1.2. The ability to develop specialized sections of project documentation, monitor implementation during the construction and operation of industrial and civil buildings
Learning outcomes: As a result of execution and completing the course work (OK 2.7), the applicant must be able to demonstrate the following learning outcomes: know: principles, relationships, algorithms, features of using the finite element method in solving problems of the mechanics of structures, in particular: - fundamentals of finite element modeling; - basic formulations of finite elements - relations in matrix form and algorithms of finite element methods for problems of statics, stability and dynamics of buildings; - methods of assessing the accuracy of solving problems using the finite element method; be able: - to formulate, analyze and solve the problems of the mechanics of structures using the finite element method, in particular: - develop finite element models of building elements; - formulate relations that describe Hermitian and Lagrangian finite elements; - calculate stiffness matrices, masses, load vectors of finite elements and the system as a whole; - apply the MSE algorithm to obtain a numerical solution to problems of statics, stability and dynamics of rod systems; - to analyze the results obtained with the use of TSE, to evaluate the accuracy of the numerical solution. Program learning results of coursework in the educational discipline OK 2.7 RN 01. Design common industrial and civil buildings and structures, including using computer design software systems. RN 06. Apply modern mathematical and numerical methods for analysis, calculation and optimization of design parameters of industrial and civil buildings and structures. RNS 1.1. Apply the acquired knowledge and understanding to identify, formulate and solve the design, construction and operation of industrial and civil objects. UM2. Ability to integrate knowledge and solve complex problems in broad or multidisciplinary contexts.
Required prior and related subjects: • Mathematical analysis; • Theoretical mechanics; • Strength of Materials; • Structural mechanics; • Stability and Dynamics of Structures
Summary of the subject: The course work involves the implementation of the FEM computational algorithm for a model problem and the FEA using FEM-FEA software.
Опис: The course work thems: FEA of frame for static load. FEA of frame with geometrically-nonlinear elements. FEA of frame with material-nonlinear elements. FEA of frame backling. Geometrically-nonlinear FEA of frame. Free vibration analysis of frame using FEM. Harmonic forced vibration analysis of frame using FEM. Time response analysis of frame for complex law of excitation. Time response analysis of frame for seismic excitation. FEA of two-dimensional stress-strain state of the plate. FEA of stress state for thin plate bending. Skills Structures discretization, finite element. Euler-Bernoulli bar-beam element. Interpolation, approximation and shape function. Stiffness matrices and equivalent loads vectors, transformation matrix. Assembling; basic algorithms for solving equations. Nonlinear FEM analysis of beams and frames. Geometric and material nonlinearities. Geometric, incremental, initial stress stiffness matrix. Linear and nonlinear buckling analysis. Plastic hinge analysis. Solving of nonlinear equations systems: incremental, iterative and mixed procedures, Newton-Raphson, arc-length method. FEM for dynamic analysis. Mass and damping matrix, Rayleigh damping. Free vibration, harmonic forced vibration. FEM for 2D problems. The plane elasticity problems. 2-D elements: formulation, approximation. 3-node triangular, 4-node quadrilateral. Isoparametric formulation, the Jacobian matrix, numerical integration. Higher order elements. Reduced integration. Plate bending and shell elements. FEM modeling techniques: choice of elements, meshing, matching and non-matching meshes; connections, supports and loads modeling, checking and solution error estimating.
Assessment methods and criteria: Coutse work: progress - 50%, CW defencing - 50%
Критерії оцінювання результатів навчання: Course work: percentage of progress, quality control. Defense of the CW: assessment abilities of solving practical structural problems using FEA. Criteria - see subsection "Procedure and criteria for issuing grades"
Порядок та критерії виставляння балів та оцінок: 88-100 points - ("excellent") - an excellent level of skills and practical skills (perfect mastery of lecture material and additional recommended literary sources, the ability to analyze phenomena in their relationship and development, correctly, succinctly, logically, consistently answer asked questions, the ability to effectively apply knowledge and skills to solve typical and atypical new problems); 71-87 points - ("good") - a good level of theoretical knowledge and practical skills (perfect mastery of lecture material, ability to analyze phenomena, correctly answer questions, ability to solve typical practical problems); 70 – 50 points – (“satisfactory”) satisfactory level of theoretical knowledge and practical skills (partial mastery of lecture material at the level of more than 50%, ability to classify phenomena, correctly answer questions, ability to solve considered basic problems); 26-49 points - ("not certified" with the possibility of repeating the semester control) - unsatisfactory knowledge - ignorance of a large part of the educational material, fundamental errors in answers to basic questions, inability to apply theoretical provisions when solving practical typical problems, errors classification of problems in solving typical problems; 00–25 points – (“unsatisfactory” with mandatory re-study) ignorance of most of the educational material, ignorance of the basic fundamental principles and theoretical provisions in answering questions, inability to navigate when solving practical problems, fundamental and essential errors in the classification of problems when solving typical problems
Recommended books: 1. Баженов В.А., Перельмутер А.В., Шишов О.В. Будівельна механіка. Комп’ютерні технології і моделювання: підручник. – К.: ПАТ “ВІПОЛ”, 2013. – 896 с. 2. Баженов В.А., Перельмутер А.В., Шишов О.В. Будівельна механіка. Комп’ютерні технології: підручник. – К.: Каравела, 2009. – 696 с. 3. Дубенець В.Г., Хільчевський В.В., Савченко О.В. Основи методу скінченних елементів: навчальний посібник. Чернігів: ЧДТУ, 2007. 287с. 4. Zienkiewicz, OC; Taylor, RL. The Finite Element Method for Solid and Structural Mechanics. 6-th ed, Elsevier Butterworth-Heinemann, 2005 . – 648p. 5. Wilson E. L. Three Dimensional Static and Dynamic Analysis of Structures. 3-rd Ed. CSI, 2002 – 423p 6. Rene De Borst, Mike A. Crisfield Nonlinear Finite Element Analysis of Solids and Structures, 2nd Ed, Wiley, 2012 – 540p.
Уніфікований додаток: Lviv Polytechnic National University ensures the realization of the right of persons with disabilities to obtain higher education. Inclusive educational services are provided by the Service of accessibility to learning opportunities "Without restrictions", the purpose of which is to provide permanent individual support for the educational process of students with disabilities and chronic diseases. An important tool for the implementation of the inclusive educational policy at the University is the Program for improving the qualifications of scientific and pedagogical workers and educational and support staff in the field of social inclusion and inclusive education. Contact at: St. Karpinsky, 2/4, 1st floor, room 112 E-mail: nolimits@lpnu.ua Websites: https://lpnu.ua/nolimits https://lpnu.ua/integration
Академічна доброчесність: The policy regarding the academic integrity of the participants of the educational process is formed on the basis of compliance with the principles of academic integrity, taking into account "Regulations on academic integrity at the Lviv Polytechnic National University" (approved by the academic council of the university on June 20, 2017, protocol No. 35).