Verification of the LIRA-FEM software

Verification of the LIRA-FEM software / Geometrically nonlinear problems for threads, cable-stayed trusses, rods, membranes and plates

Тест 3.1 Steel wire rope with a specified pitch

Analytical Solution: The Designer's Handbook of Calculation and Theory, ed. by Prof. A.A. Umansky, Moscow: "Construction Publishing House", 1960, pp. 321 - 327.
For the construction of the scheme was used FE 310 (geometrically non-linear rod FE). Number of nodes:101. Number of elements:100.

Тест 3.2 Thread with multi-trunk supports

Analytical Solution: Designer's Handbook, M.: "building edition", 1972, vol.1, pp. 582 - 583.
To build the scheme we used FE 310 (geometrically non-linear rod FE) and FE 51 (single-node FE). Number of nodes:102. Number of elements:102.

Тест 3.3 Steel wire rope with a given initial length

Analytical solution: L.G. Dmitriev, A.V. Kasilov Cable Covers (Calculation and Construction), Publishing House " Builder", Kiev, 1968, pp. 66 - 70.
To build the scheme we used FE 310 (geometrically non-linear rod FE) and FE 51 (single-node FE). Number of nodes:102. Number of elements:102.

Тест 3.4 Cableway network

Analytical solution: L. G. Dmitriev, A. V. Kasilov Cable Covers (Calculation and Construction), Publishing house "Budivelnik", Kiev, 1968, стр. 71 – 74.
For the construction of the scheme was used FE 310 (geometrically non-linear rod FE). Number of nodes:12. Number of elements:12.

Тест 3.5 Cable Truss

Analytical solution: L. G. Dmitriev, A. V. Kasilov Cable Covers (Calculation and Construction), Publishers "Budivelnik", Kiev, 1968, pp. 75 - 81.
For the construction of the scheme was used FE 310 (geometrically non-linear rod FE). Number of nodes:12. Number of elements:12.

Тест 3.6 Strong bending of the console

Analytical solution: L. D. Landau, E. M. Lifshitz Theory of Elasticity, M.: Nauka, 1987, p. 106.
To build the circuit we used FE 309 (geometrically nonlinear rod FE) and FE 341 (geometrically nonlinear rectangular FE). Number of nodes:303. Number of elements:200.

Тест 3.7 Zacritic bending of the console

Analytical solution: L. D. Landau, E. M. Lifshits Theory of Elasticity, M.: "Science", 1987, p. 107. 107.
For the construction of the scheme was used FE 309 (geometrically non-linear rod FE). Number of nodes:101. Number of elements:100.

Тест 3.8 Zacritical bending of an articulated rod

Analytical solution: L. D. Landau, E. M. Lifshits Theory of Elasticity, M.: "Science", 1987, p. 107. 107.
For the construction of the scheme was used FE 309 (geometrically non-linear rod FE). Number of nodes:101. Number of elements:100.

Тест 3.9 Geometrically nonlinear problem with rods of different stiffness

Analytical solution: G. N. Vanderplaats, Numerical Optimization Techniques for Engineering Design with Applications, McGraw-Hill Book Co., Inc., New York, NY, 1984, pp. 72-73, ex. 3-1.
For the construction of the scheme was used FE 310 (geometrically non-linear rod FE). Number of nodes:3. Number of elements:2.

Тест 3.10 Rod under tension and uniformly distributed load

Analytical solution: S. Timoshenko, Strength of Material, Part II, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pg. 42, article 6.
For the construction of the scheme was used FE 310 (geometrically non-linear rod FE). Number of nodes:22. Number of elements:20.

Тест 3.11 Strong bending of the cantilever plate

Analytical solution: K. J. Bathe, E. N. Dvorkin, “A Formulation of General Shell Elements - The Use of Mixed Interpolation of Tensorial Components”, Int. Journal for Numerical Methods in Engineering,...
For the construction of the scheme was used FE 341 (geometrically non-linear rectangular FE). Number of nodes:303. Number of elements:200.

Тест 3.12 Square diaphragm with pliable contour

Source: Yeremeev P. G., Prisyazhnoi V. B. Experimental studies of square membranes with pliable contour. // Structural Mechanics and Design of Structures, pp. 58 - 61.
To build the circuit we used FE 309 (geometrically nonlinear rod FE) and FE 341 (geometrically nonlinear rectangular FE). Number of nodes:1681. Number of elements:1680.

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