An approach to the optimization of thin-walled cantilever open section beams

U ovom radu je razmatran jedan pristup optimizaciji tankozidih konzolnih konstrukcionih elemenata otvorenih poprečnih preseka izloženih savijanju i ograničenoj torziji. Problem je redukovan na određivanje minimalne mase t.j. minimalne površine konstrukcionih tankozidih elemenata oblika I i U-profila za zadata opterećenja, materijal i geometrijske karakteristike. Površina poprečnog preseka nosaca je izabrana za funkciju cilja. Uvedeno je naponsko ograničenje. Primenom metode Lagranžovog množitelja formirane su jednačine čija rešenja predstavljaju optimalne odnose dimenzija poprečnog preseka izabranog oblika. Dobijeni rezultati su iskorišćeni pri numeričkom proračunu.An approach to the optimization of the thin-walled cantilever open section beams subjected to the bending and to the constrained torsion is considered. The problem is reduced to the determination of minimum mass, i.e. minimum cross-sectional area of structural thin-walled I-beam and channel-section beam elements for given loads, material and geometrical characteristics. The area of the cross-section is assumed to be the objective function. The stress constraints are introduced. Applying the Lagrange multiplier method the equations, whose solutions represent the optimal values of the ratios of the parts of the chosen cross-section, are formed. The obtained results are used for numerical calculation

Stress constraints applied to the optimization of a thin-walled Z-beam

Razmatran je jedan pristup optimizaciji tankozidih otvorenih poprečnih preseka oblika Z - profila, izloženih savijanju i ograničenoj torziji. Za data opterećenja, materijal i geometrijske karakteristike, problem se svodi na određivanje minimalne mase, odnosno minimalne površine poprečnog preseka konstruktivnih tankozidih poprečnih preseka izabranog oblika. Površina poprečnog preseka je izabrana za funkciju cilja. Uvedena su naponska ograničenja. Primenjuje se Metoda Lagranžovog množitelja. Rezultati analitički dobijenih jednačina za matematički model, numerička rešenja, kao i ušteda u masi, izračunati su za tri slučaja opterećenja. Neki rezultati su provereni primenom programa COSMOS.One approach to the optimization of a thin-walled open section Z-beam subjected to the bending and to the constrained torsion is considered. For given loads, material and geometrical characteristics, the problem is reduced to the determination of minimum mass i.e. minimum crosssectional area of structural thin-walled beam of the chosen shape. The area of the cross-section is assumed to be the objective function. The stress constraints are introduced. The Lagrange multiplier method is applied. Solutions of analitically obtained expressions for the mathematical model, numerical solutions, as well as the saved mass, are calculated for three loading cases

Mathematical modelling and multicriteria design optimization of a thin-walled beam

One approach to the optimization of a thin-walled open section beam subjected to complex loads is considered. For given loads, material and geometrical characteristics the problem is reduced to the determination of minimum mass i.e. minimum cross-sectional area of thin-walled beam and minimum of safety factor for the given construction. A method is described to solve a nonlinear parameter optimization problem with several objective functions. In the present work, multicriteria optimization technique is introduced to extremise simultaneously several objective functions. For the defined multicriteria optimization model, a computer program based on interactive dialogue was developed. The graphical illustration of the above problem is presented in terms of objective function

Stress constraints applied to the optimization of a thin-walled Z-beam

Razmatran je jedan pristup optimizaciji tankozidih otvorenih poprečnih preseka oblika Z - profila, izloženih savijanju i ograničenoj torziji. Za data opterećenja, materijal i geometrijske karakteristike, problem se svodi na određivanje minimalne mase, odnosno minimalne površine poprečnog preseka konstruktivnih tankozidih poprečnih preseka izabranog oblika. Površina poprečnog preseka je izabrana za funkciju cilja. Uvedena su naponska ograničenja. Primenjuje se Metoda Lagranžovog množitelja. Rezultati analitički dobijenih jednačina za matematički model, numerička rešenja, kao i ušteda u masi, izračunati su za tri slučaja opterećenja. Neki rezultati su provereni primenom programa COSMOS.One approach to the optimization of a thin-walled open section Z-beam subjected to the bending and to the constrained torsion is considered. For given loads, material and geometrical characteristics, the problem is reduced to the determination of minimum mass i.e. minimum crosssectional area of structural thin-walled beam of the chosen shape. The area of the cross-section is assumed to be the objective function. The stress constraints are introduced. The Lagrange multiplier method is applied. Solutions of analitically obtained expressions for the mathematical model, numerical solutions, as well as the saved mass, are calculated for three loading cases

Numerical calculation of the water-tube boiler using finite element of the orthotropic plate

Norme uglavnom pokrivaju proračun delova pod pritiskom, ali uglavnom bez uticaja termičkih opterećenja. Primena metode konačnih elemenata predlaže se pri proračunu svih komponenti koje norme ne obuhvataju. U radu je prikazan detaljan numerički proračun vodocevnog kotla tipa VU60 - Minel kotlogradnja. Na osnovu numeričkih modela određena su polja napona i deformacija za različita opterećenja. Razmatran je uticaj natpritiska i termičkog opterećenja. Primenjeni su i parametri dijagnostike čvrstoće kao što su raspodela membranskih i savojnih napona po podstrukturama i raspodela energije deformacije. Membranski zidovi (cevni paneli) vodocevnih kotlova izloženi su veoma velikim opterećenjima. Modelirani su elementima tanke ortotropne ploče. Razmotren je uticaj pojaseva ukrućenja na ponašanje konstrukcije kotla.Norms handle the issues concerned with calculation of pressurized boiler components, however not considering the influences of thermal strains. Application of FEM in boiler design is suggested in calculating all components that are not covered by the norm. Detailed numerical calculation of the water-tube boiler type VU60-Minel Kotlogradnja is presented in the paper. Stress and strain fields are obtained based on numerical models for various types of loading. The influences of the over-pressure and thermal loading are discussed. Distribution of membrane and bending stresses for substructures and distribution of deformation energy are involved in the analysis. Membrane walls (tube panels) of the water-tube boilers are exposed to large loads. They are modelled using elements of a thin orthotropic plate. The influence of the buck-stays on the structural behaviour is discussed

Numerical calculation of the water-tube boiler using finite element of the orthotropic plate

Norme uglavnom pokrivaju proračun delova pod pritiskom, ali uglavnom bez uticaja termičkih opterećenja. Primena metode konačnih elemenata predlaže se pri proračunu svih komponenti koje norme ne obuhvataju. U radu je prikazan detaljan numerički proračun vodocevnog kotla tipa VU60 - Minel kotlogradnja. Na osnovu numeričkih modela određena su polja napona i deformacija za različita opterećenja. Razmatran je uticaj natpritiska i termičkog opterećenja. Primenjeni su i parametri dijagnostike čvrstoće kao što su raspodela membranskih i savojnih napona po podstrukturama i raspodela energije deformacije. Membranski zidovi (cevni paneli) vodocevnih kotlova izloženi su veoma velikim opterećenjima. Modelirani su elementima tanke ortotropne ploče. Razmotren je uticaj pojaseva ukrućenja na ponašanje konstrukcije kotla.Norms handle the issues concerned with calculation of pressurized boiler components, however not considering the influences of thermal strains. Application of FEM in boiler design is suggested in calculating all components that are not covered by the norm. Detailed numerical calculation of the water-tube boiler type VU60-Minel Kotlogradnja is presented in the paper. Stress and strain fields are obtained based on numerical models for various types of loading. The influences of the over-pressure and thermal loading are discussed. Distribution of membrane and bending stresses for substructures and distribution of deformation energy are involved in the analysis. Membrane walls (tube panels) of the water-tube boilers are exposed to large loads. They are modelled using elements of a thin orthotropic plate. The influence of the buck-stays on the structural behaviour is discussed

The optimization of a thin walled I-beam subjected to displacement constraint

One approach to the optimization of a thin walled cantilever I-beam subjected to constrained torsion is considered. The aim of this paper is the determination of the minimum mass i.e. minimum cross sectional area of structural thin-walled I-beam elements for given loads, material and geometrical characteristics. That is why the area of the cross section is assumed to be the objective function. The displacement constraints are introduced: allowable angle of twist and allowable angle of twist per unit length. The starting points during the formulation of the basic mathematical model are the assumptions of the thin walled beam theory from one side and the basic assumptions of the optimum design from the other. Applying the Lagrange multiplier method, the equation of the second order, which solutions represent the optimal values of the ratios of the parts of the chosen cross section, is formed. The obtained results are used for numerical calculation applying The Finite Element Method

Dynamic behavior of the elements of gear-box

Dynamic behavior of the elements of gear-box was defined based on the dynamic calculation realized by finite element method. Frequencies and appropriate deformation fields (oscillations) were obtained by using program package KOMIPS. All structures of the considered construction of the gear-box were involved in calculation: cover, input- shaft, middle-shaft and output-shaft. Modeling was done by using plate (shell) and volume finite elements

Modeling of the buckstay system of membrane walls in watertube boiler construction

Membrane walls are very important structural parts of water-tube boiler construction. Based on their specific geometry, one special type of finite element was defined to help model the global boiler construction. That is the element of reduced orthotropic plate with two thicknesses and two elasticity matrixes, for membrane and bending load separately. A global model of the boiler construction showed that the high value of stress is concentrated in plates of the buckstay system in boiler corners. Validation of the new finite element was done on the local model of the part of membrane wall and buckstay. A very precise model of tubes and flanges was compared to the model formed on the element of a reduced orthotropic plate. Pressure and thermal loads were discussed. Obtained results indicated that the defined finite element was quite favorable in the design and reconstruction of the boiler substructures such as a buckstay system