Verification of the LIRA-FEM software

Verification of the LIRA-FEM software / Linear static problems for rod systems, plates and shells, three-dimensional problems

Test 1.1 Space frame with elastic supports

Analytical solution: M. Laredo,Sistance des matriaux, Paris, Dunod, 1970, p. 165.
To build the scheme, FE 10 (bar FE) and FE 51 (single-node FE) are used. Number of nodes:5. Number of elements:10.

Test 1.2 Flat Truss

Analytical solution: M. Laredo, Résistance des matériaux, Paris, Dunod, 1970, p. 579.
For the construction of the scheme used KE 1 (rod KE). Number of nodes:9. Number of elements:10.

Тест 1.3 Beam with tightener

Analytical solution: M. Laredo, Résistance des matériaux, Paris, Dunod, 1970, p. 77.
To build the circuit we used FE 1 (rod FE) and KE 10 (rod FE). Number of nodes:9. Number of elements:10.

Тест 1.4 Rectangular plate

Analytical solution: S. Timoshenko, Résistance des matériaux, t. 1, Paris, Librairie Polytechnique Ch. Béranger, 1949.
For the construction of the scheme used FE 11 (lamellar FE). Number of nodes:1111. Number of elements:1000.

Тест 1.5 Round plate

Analytical solution: S. Timoshenko, Résistance des matériaux, t. 2, Paris, Librairie Polytechnique Ch. Béranger, 1949.
For the construction of the scheme used KE 11 (lamellar KE). Number of nodes:1111. Number of elements:1000.

Тест 1.6 Cylinder under internal pressure

Analytical solution: R.J. Roark et W.C. Young, Formulas for stress and strain, 5e edition, New York, McGraw-Hill, 1975.
For the construction of the scheme used FE 44 (quadrangular FE). Number of nodes:504. Number of elements:480.

Тест 1.7 Thor under internal pressure

Analytical solution: R.J. Roark et W.C. Young, Formulas for stress and strain, 5e edition, New York, McGraw-Hill, 1975.
For the construction of the circuit we used FE 44 (quadrangular FE). Number of nodes:304. Number of elements:288.

Тест 1.8 Cylindrical shell under its own weight

Analytical solution: A.C. Scordelis et K.S. Lo, “Computer analysis of cylindrical shells”, J. Amer. Concr. Inst., 61, 1964.
For the construction of the scheme used KE 41 (rectangular KE) . Number of nodes:441. Number of elements:400.

Тест 1.9 Cantilever plate under the action of a pair of forces

Analytical solution: J. Robinson, Element evaluation. A set of assessment parts and tests, Proceeding of Finite Element Methods in the commercial environment, vol. 1, octobre 1978. J.L. Batoz et M.B....
For the construction of the scheme used FE 41 (rectangular FE) . Number of nodes:867. Number of elements:800.

Тест 1.10 The parallelepiped under the action of its own weight

Analytical solution: S. Timoshenko, Théorie de l’élasticité, Paris, Librairie Polytechnique Ch. Béranger, 1961, pages 279 – 282.
For constructing the scheme used KE 41 (rectangular KE) and KE 31 (parallelepiped). Number of nodes:325. Number of elements:208.

Тест 1.11 Pure bending of the prismatic bar

Analytical solution: S. Timoshenko, Théorie de l’élasticité, Paris, Librairie Polytechnique Ch. Béranger, 1961, pages 284 – 289.
For constructing the scheme used KE 41 (rectangular FE) and FE 31 (parallelepiped). Number of nodes:325. Number of elements:208.

Тест 1.12 Round thick slab

Analytical Solution: S.P. Timoshenko, S. Voynovsky-Krieger. Plates and Shells. GIF-ML, Moscow, 1963. p.73-90
For the construction of the scheme were used FE 44 (quadrangular FE) and FE 42 (triangular FE) . Number of nodes: 32766. Number of elements:32400.

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