Verification of the LIRA-FEM software

Verification of the LIRA-FEM software / Static and dynamic problems with one-sided constraints

Тест 7.1 Cantilever bar on single-sided supports

Analytical solution: A. V. Perelmuter, V. I. Slivker Calculation models of structures and the possibility of their analysis, Kiev: "Steel", 2002, p. 122.
To build the circuit, the FE 10 (rod FE) and KE 261 (single-node FE) are used. Number of nodes:13. Number of elements:15.

Тест 7.2 System with single-sided springs

Analytical solution: A. V. Perelmuter, V. I. Slivker Calculation models of structures and the possibility of their analysis, Kiev: "Steel", 2002, p. 123.
To build the circuit, the FE 10 (rod FE) and FE 261 (single-node FE) are used. Number of nodes:13. Number of elements:15.

Тест 7.3 Round plate on a single-sided elastic base

Analytical and numerical solutions: P. Panagiotopoulos Inequalities in Mechanics and their Applications, Moscow: Mir, 1989, p. 384.
To build the circuit we used FE 42 (triangular FE), FE 44 (quadrangular FE) and SE 261 (single-node FE). Number of nodes:201. Number of elements: 299.

Тест 7.4 Contact problem for a cylinder

Numerical solution: P. Panagiotopoulos Inequalities in Mechanics and their Applications, Moscow: Mir, 1989, p. 387.
To build the scheme used FE 10 (rod FE) and KE 262 (two-node FE). Number of nodes:182. Number of elements:361.

Тест 7.5 Square plate on a one-sided rigid base

Numerical solution: P. Panagiotopoulos Inequalities in Mechanics and their Applications, Moscow: Mir, 1989, p. 367.
To build the scheme used FE 10 (rod FE) and KE 262 (two-node FE). Number of nodes:182. Number of elements:361.

Тест 7.6 Temperature expansion in the presence of a gap

Analytical solution: C. O. Harris, Introduction to Stress Analysis, The Macmillan Co., New York, NY, 1959, pg. 58, problem 8.
To build the circuit, the KE 10 (rod FE) and FE 261 (single-node FE) are used. Number of nodes:3. Number of elements:3.

Тест 7.7 Dynamic one-sided contact problem for a square plate

Numerical solution: P. Panagiotopoulos Inequalities in Mechanics and their Applications, Moscow: Mir, 1989, pp. 408 - 415.
For the construction of the scheme used FE 11(rectangular FE). Number of nodes:2601. Number of elements:2500.

Verification examples


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