Calculation of Reinforced Concrete Prismatic Shells by the Finite Element Method Using Variable Elasticity Parameters


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The paper considers the modification of the generally accepted formulation of the finite elements method by applying in the calculation I.Mileykovski’s refined technical theory of shells that takes into account the deformations of the transverse shear along the thickness of the model. When applying this solution path, it is possible to calculate thick and thin shells (plates) with equal efficiency, taking into account the complex strained state of an anisotropic material. It illustrates the inclusion in the computational algorithm of variable parameters of the elasticity of concrete, allowing more accurate evaluation of the stress-strain state in the finite element under complex (combined) loads. The presence of reinforcement in the material is modeled by dividing the structure into layers and sequentially reduction the elastic characteristics of the material based on the volume ratio of the components. The advantage of the algorithm is the ease of its integration with the conventional finite elements method. All transformations in this case consist in the modification of expressions for determining the elastic characteristics of the construction, calculating the gradient and stiffness matrices, while the sequence of further calculations does not change. This enables to use the proposed algorithm, including as a plug-in software module, expanding the capabilities of existing computing programs. The article demonstrates the application of the method in modeling a reinforced concrete slab made with the use of multi-component high-strength concrete of a heavy class having a prismatic strength under uniaxial compression of more than 110 MPa.



Edited by:

Dr. Denis Solovev




V. Kruglov and V. Iurchenko, "Calculation of Reinforced Concrete Prismatic Shells by the Finite Element Method Using Variable Elasticity Parameters", Materials Science Forum, Vol. 945, pp. 969-974, 2019

Online since:

February 2019




[1] O.Y. Berg, Strength of concrete and other materials with different tensile and compressive strengths under conditions of a complex stress state, Studies of concrete and reinforced concrete structures of transport structures. (1960) 5-41.

[2] A.N. Zhirenkov, Deformation and strength of ordinary heavy concrete in a complex stress state, diss. Dr. Techn. Sciences, Moscow, (2009).

[3] L.K. Luksha, Calculation of the strength of reinforced concrete structures taking into account the complex stress state of concrete, diss. ... Dr. Techn. Sciences, Moscow, (1980).

[4] R.A. Arutyunyan, On the account of the Bauschinger effect and volume plastic deformation in the plasticity theory, Investigations on Elasticity and Plasticity. (1968) 87-93.

[5] P.M. Beech, Deformability of Concrete in Flat Stressed States, Building Structures and Structural Theory. (1977) 87-92.

[6] A.V. Zenin, Determination of the stress-strain state of elements of bridge reinforced concrete structures taking into account the properties of materials and the nature of loading, diss. ... Cand. Tech. Sciences, Novosibirsk, 1987. 198 p.

[7] I.I. Kulik, Strength, deformation of concrete and the calculation of reinforced concrete structures in the case of a plane stressed state, diss. Cand. Tech. Sciences, (1982).

[8] M.B. Lifshits, The account of a tense condition in the criteria of strength of concrete, Building structures of transport purpose, (1979) 19-30.

[9] A.A. Petrov, Deformation model of nonlinear creep of reinforced concrete and its application to the calculation of plane-stressed elements and systems of them, diss. Dr. Techn. Sciences, Moscow, (2001).

[10] V.V. Novozhilov, On the relationship between stresses and strains in a nonlinearly elastic medium, PMM, T. 15. (1951) 183-194.

[11] P.I. Vasil'ev, Nonlinear deformation of creep of concrete, Izv. VNIIG, T. 95 (1971) 59-69.

[12] A.V. Ermakova, A method of additional finite elements for the nonlinear calculation of reinforced concrete structures by limiting states, ASV, Moscow, (2017).

[13] V.M. Kruglov, Nonlinear resistance of elements of reinforced concrete bridge structures, diss. ... Dr. Techn. Sciences, Novosibirsk, (1988).

[14] N.I. Karpenko, V.M. Kruglov, L.Y. Soloviev, Nonlinear deformation of concrete and reinforced concrete, STU, Novosibirsk, (2001).

[15] V.E. Iurchenko, Strength Criteria of Modified Concretes in Flat Tension, Vestnik RSTU. 2/2015 (2015) 110-115.

[16] N.I. Bezukhov, Fundamentals of the Theory of Elasticity, Plasticity and Creep, Higher School, Moscow, (1982).

[17] V.M. Kruglov, V.E. Iurchenko, On one approach in constructing the basic physical relationships of concrete in a plane stressed state, Vestnik RSTU. 2/2016 (2016) 102-110.

[18] V.M. Kruglov, A.I. Kozachevsky, Basic physical relationships for concrete in a plane stress state, Resistance of materials and theory of structures. (1988) 25-32.

[19] V.M. Kruglov, Stiffness characteristics of three-dimensional reinforced concrete elements with cracks, Reliability and durability of man-made structures of railway transport. (1990) 38-51.

[20] I.E Milejkovski, A system of initial equations of shallow shells with allowance for the thickness shift and their solution by the finite element method, Spatial constructions of buildings and structures. (1974) 5-10.

[21] A.V. Khvastunov, Powder-activated high-strength concrete and fiber-reinforced concrete with low consumption of cement per strength unit, diss. ... Cand. Tech. Sciences, Penza, (2011).

[22] V.S. Zyryanov, Recommendations for the calculation and design of prefabricated solid slabs for residential and public buildings, Central Research Institute for Housing, Moscow, (2005).

[23] Code of Regulations SP 52-101-2003 Concrete and reinforced concrete structures without prestress of reinforcement,, Gosstroy of Russia, Moscow, (2003).