Optimization of flat steel frame and foundation posts system

Alekseytsev, Anatoly; Serpik, I. N.

doi:10.5862/mce.61.2

Cited by 15 publications

(9 citation statements)

References 5 publications

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“…Calculations of individual examples showed the presence of extreme points in the dependence found, which makes possible some optimization of the rigidity design. There are known works on optimization of trusses for rigidity, economy, strength and stability [6][7][8][9]. The obtained analytical formulas with sufficiently simple polynomial coefficients can supplement these results or evaluate their…”

Section: Discussionmentioning

confidence: 99%

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Analytical calculation of the deflection of the lattice truss

Kirsanov

Tinkov

2018

MATEC Web Conf.

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Abstract. An algorithm is given for deriving the dependence of the deflection of a planar statically determinate beam truss on the number of panels, dimensions and load. Three load cases are considered: uniform load on the lower belt, upper belt and vertical force in the middle of the span. By induction, generalizing a series of solutions for trusses with a consecutively increasing number of panels, the desired formula is obtained for the deflection and horizontal displacement of the mobile support of the truss. All transformations are performed in the system of symbolic mathematics Maple. For a sequence of coefficients of the desired formula, using the special Maple operators, homogeneous recurrent equations are constructed and solved. The coefficients found are in the form of polynomials in the number of panels. The asymptotic property of the solution is found. On the graphs of the dependence of the deflection on the number of panels and on the height, extreme points are found. The solution can be used to test the calculations obtained numerically.

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Section: Discussionmentioning

confidence: 99%

“…Optimization problems are also solved numerically [6][7][8][9]. Analytical calculations of building structures are quite rare, and the formulas on which they are based generally have a narrow field of application.…”

Section: Introductionmentioning

confidence: 99%

Analytical calculation of the deflection of the lattice truss

Kirsanov

Tinkov

2018

MATEC Web Conf.

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“…With the advent in the mid 80s of the last century computer mathematics systems in engineering practice for the calculation of building structures, it became possible to use not only numerical methods [1][2][3][4][5][6][7][8][9], but also analytical methods. The very first samples in this direction were reduced to obtaining formulas for calculations of deflection and stresses in a concrete design with a parametric representation of the load, dimensions, and elastic properties of the material.…”

Section: Introductionmentioning

confidence: 99%

Analytical calculation of the combined suspension truss

2019

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An algorithm is given for obtaining the formula for the dependence of the deflection of a regular planar truss of an arched type with a suspended lower belt on the number of panels. The cases of uniform loading of the nodes of the upper and lower belts by a vertical load are considered. To generalize a number of solutions obtained in the system of computer mathematics Maple to an arbitrary case, an induction method was applied. For this purpose, for a sequence of coefficients of the particular solutions found, a common term is determined which is a solution of the recurrence equation. The deflection was determined with the help of Mohr's integral, which depends on the forces in the rods. Forces in a statically determinate construction were performed by cutting out nodes from the solution of a system of equations written in a matrix form. The analytical dependence of displacement of the mobile support on the number of panels is found.

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“…Then the engineer by the formulas can pick up not only the sizes of a design, but also the optimum number of panels. Such problems arise when solving optimization problems [6][7][8][9]. In this paper, we propose an inductive approach for deriving the formulas for the dependence of the planar truss bending on the number of panels.…”

Section: Introductionmentioning

confidence: 99%

Inductive analysis of the deflection of a beam truss allowing kinematic variation

2018

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A scheme of a statically determinate planar truss is proposed and an analytical calculation of its deflection and displacement of the mobile support are obtained. The forces in the rods from the external load, uniformly distributed over the nodes of the lower or upper belt, are determined by the method of cutting out nodes using the computer mathematic system Maple. In the generalization of a number of solutions of trusses with a different number of panels to the general case, the general terms of the sequence of coefficients in the formulas are found from solutions of linear homogeneous recurrence equations. To compose and solve these equations, Maple operators were used. In the process of calculation it was revealed that for even numbers of panels in half the span, the determinant of the system of equations degenerates. This corresponds to the kinematic degeneracy of the structure. The corresponding scheme of possible speeds of the truss is given. The displacement was determined by the Maxwell-Mohr’s formula. The graphs of the obtained dependences have appreciable jumps, which in principle can be used in the selection of optimal design sizes.

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Optimization of flat steel frame and foundation posts system

Cited by 15 publications

References 5 publications

Analytical calculation of the deflection of the lattice truss

Analytical calculation of the deflection of the lattice truss

Analytical calculation of the combined suspension truss

Inductive analysis of the deflection of a beam truss allowing kinematic variation

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