• knowledge of the finite element methods principles and theory;
• knowledge of the FEM application for static, stability and dynamics analysis of structures;
• knowledge of the basical FEM modeling techniques, checking and solution error estimating;
• skills and abilities to carry out finite element analysis of structures.

• Mathematical analysis;
• Theoretical mechanics;
• Strength of Materials;
• Structural mechanics;
• Stability and Dynamics of Structures

Basis. Boundary value problem formulation, variational formulation of boundary value 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.

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. Зенкевич О. Метод конечных элементов в технике: Пер. с англ. –М.: Мир, 1975. – 541с.
5. Галлагер Р. Метод конечных элементов. Основы. М.:Мир, 1984. 423с.
6. Баженов В. А., Дащенко А. Ф., Коломиец Л. В., Оробей В. Ф. Строительная механика. Специальный курс. Применение метода граничных елементов. – Одесса: “Астропринт”, 2001. – 580с.
7. Zienkiewicz, OC; Taylor, RL. The Finite Element Method for Solid and Structural Mechanics. 6-th ed, Elsevier Butterworth-Heinemann, 2005 . – 648p.
8. Wilson E. L. Three Dimensional Static and Dynamic Analysis of Structures. 3-rd Ed. CSI, 2002 – 423p
9. Rene De Borst, Mike A. Crisfield Nonlinear Finite Element Analysis of Solids and Structures, 2nd Ed, Wiley, 2012 – 540p.

Сlasses, tutorials - 50 %;
written exam - 50%.

The ability and skills to solve problems of statics, dynamics and stability of structures using finite element method (FEM): to analyze and formulate the problem; choose, build and apply suitable finite element types; perform FEM calculations; interpret and analyze the results of calculations, analyze the stability and convergence of algorithms and method, to estimate the error of solution.

• Mathematical analysis;
• Theoretical mechanics;
• Strength of Materials;
• Structural mechanics;
• Stability and Dynamics of structures;
• Finite Element Method for Structural Analysis

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.

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. Дубенець В.Г., Хільчевський В.В., Савченко О.В. Основи методу скінченних елементів: навчальний посібник. Чернігів: ЧДТУ, 2007. 287с.
3. Зенкевич О. Метод конечных элементов в технике: Пер. с англ. –М.: Мир, 1975. – 541с.
4. Галлагер Р. Метод конечных элементов. Основы. М.:Мир, 1984. 423с.
5. Zienkiewicz, OC; Taylor, RL. The Finite Element Method for Solid and Structural Mechanics. 6-th ed, Elsevier Butterworth-Heinemann, 2005 . – 648p.
6. Wilson E. L. Three Dimensional Static and Dynamic Analysis of Structures. 3-rd Ed. CSI, 2002 – 423p
7. Rene De Borst, Mike A. Crisfield Nonlinear Finite Element Analysis of Solids and Structures, 2nd Ed, Wiley, 2012 – 540p.

The course work execution and defendce - 100%