Course details

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Theory of structures

Teaching:
ECTS:
Level:
Semester:
Prerequisites:
None
Load:
Lectures Exercises Laboratory exercises Project laboratory Physical education excercises Field exercises Seminar Design exercises Practicum
45 0 30 0 0 0 0 0
Course objectives:
Introduction to basic structural elements of ship structures. Definition of the strength related problems and their dimensioning according to strength criterion. Application of the relevant analytical and numerical methods. Introduction to the basics of the theory of vibrations and explanation of the methods for vibrational analysis of discrete vibration systems.
Student responsibilities:
Grading and evaluation of student work over the course of instruction and at a final exam:
4 colloquiums + oral exam. or Written exam + oral exam.
Methods of monitoring quality that ensure acquisition of exit competences:
Students questionnaire.
Upon successful completion of the course, students will be able to (learning outcomes):
After successfully completing the lectures, students will be able to: - analyze and solve problems of static and dynamic analysis of structural elements of ship structures by analytical and numerical methods, - calculate the stresses and determine the dimensions of the structure based on give loading, - formulate reliable calculation models of real structural elements of ship structures, - estimate the nature of real irregular loading and describe it with adequate loading used in calculations, - clear up the protocol of ship vibration analysis, - analyze free vibrations, natural frequencies and mode shapes of vibration systems, - analyze forced vibrations and amplitude of response of discrete vibration systems, - estimate the first natural frequency of complex continuous vibration systems.
Lectures
1. Differential equation of the membrane, differential equation of the rectangular plate bending, Ritz energy method for the plate.
2. Method of finite differences (MFD) in general and the application on 1D problems (rod, shaft, beam).
3. Application of the MFD to 2D problems (membrane, plate).
4. Finite element method (FEM) in general and the application on 1D problems (rod, shaft, beam).
5. Application of the FEM to 2D problems (membrane, plate).
6. Application of the FEM for the analysis of the structures comprised of different element types.
7. Complex differential equation of axisymmetricall shells, approximate method of the equation solution by asymptotic integration, the principle of disregarding the edge influence.
8. Analysis of the particular types of shells (cylindrical, conical, spherical, circular plate with and without the opening), connection of different types of shell.
9. Vibrational system with one degree of freedom; analysis of free vibrations; properties of the harmonic motion.
10. Analysis of the forced vibrations with and without damping; harmonic excitation force (direct excitation force, centrifugal excitation force, excitation of the base); principle of operation of the instruments for vibration measurement.
11. Periodic excitation force and periodic vibrations; harmonical analysis of periodic vibrations, spectrum of the frequency response.
12. Impuls excitation force, transient vibrations; approximate method of the peak response by the method of integration of the excitation force.
13. Vibration system with two degrees of freedom; frequency equation of the free vibrations, natural frequencies and natural modes of vibrations.
14. Forced vibrations analysis, direct method and the method of modal superposition, flexural vibrations, method of influential coefficients.
15. Vibration system with multiple degrees of freedom and continuous systems; determination of the first natural frequency by the method of Rayleigh quotient.
Exercises
1. The example of rectangular plate with articulated and fixed support, various types of loading, displacement function in the form of polynomial and trigonometric functions.
2. Rod, shaft and beam loaded with concentrated forces and moments, as well as continuous load, with different types of supports.
3. Rectangular plate subjected to various loads and with different types of support.
4. Rod, shaft and beam subjected to various loads and with different types of support.
5. Membrane and plate loaded with continuous and concentrated forces with different types of support.
6. Construction assembled trough a combination of rods and beams, rods and membranes and beams and plates with various types of loading.
7. The example of cylindrical shell and the example of differential equation solution on that example. Determination of the forces and displacements with and without neglecting of the edge influence.
8. The example of conical shell with upper and lower edge, the example of spherical shell with and without the edge, example of the circular plate with and without the edge, example of the shell and circular plate connection and the example of the two shells connection.
9. Determination of the harmonic motion for the given initial conditions.
10. Calculation of the amplitude of vibrations and the phase shift for various harmonic excitations.
11. Analysis of the response function through the harmonical analysis of the given periodical excitation force; harmonic analysis of the given periodic response function, harmonic analysis of the measured results of periodic vibrations.
12. Determination of the response due to a long and short term excitation forces, i.e. in the phase of the acting of the force and the phase after the force is active; application of the approximate method for determination of the maximum response in the case of short term excitation force.
13. Determination of the natural frequencies and natural mode shapes; verification of the results by the application of the mode shape orthogonality.
14. Determination of the amplitude of vibration by application of both direct method and modal superposition method; analysis of flexural vibration system with a particular emphasis on the determination of the influential coefficients.
15. Application of different forms of Rayleigh quotient for multiple degree-of-freedom and continuous vibration systems, comparison with the exact solution.
Compulsory literature:
Grubišić, R.: Teorija konstrukcija, primjeri statičke analize elemenata konstrukcije, Sveučilište u Zagrebu - FSB, Zagreb, 1998.
Grubišić, R.: Teorija konstrukcija, primjeri dinamičke analize elemenata konstrukcija, Sveučilište u Zagrebu - FSB, Zagreb, 2002.
Senjanović, I.: Metoda konačnih elemenata u analizi brodskih konstrukcija, Sveučilište u Zagrebu - FSB, Zagreb, 1998.
Recommended literature:

Faculty of Mechanical Engineering
and Naval Architecture
Ivana Lučića 5
10002 Zagreb, p.p. 102
Croatia
MB 3276546
OIB 22910368449
PIC 996827485
IBAN HR4723600001101346933
tel: +385 1 6168 222
fax: +385 1 6156 940
University of Zagreb
Ministry of Science and Education