Implementation in Fortran90 of Finite Element Procedures for the linear static analysis of 2D planar structures. Available models implemented are the unidirectional truss finite element and Euler-Bernoulli beam finite element.
The main program, which can be compiled with any Fortran compiler and here provided, is written in Fortran90 programming language, and contains the specific subroutines for the linear static analysis of a planar beam structure. The code is distributed in different files, including both necessary subroutines for truss elements and Euler beam elements. The main structure of the code is here described, in the Source/ folder one can find:
- PROG_Main.f90: contains the main program procedure, the element type selection procedure and the subsequent subroutine calling for the computation of physical quantities and solution of the linear system of equations;
- MOD_Data.f90: contains the main module MOD_DATA, in which the main information about the two different finite elements are defined, the global variables in both cases are declared and internal variables are initialized;
- PRE_Preprocessor.f90: contains subroutines PREPROCESSING, both for truss and Euler beam finite elements, in these subroutine the global (enumerated) nodes list, the definition of elements by its connectivity, material properties, and boundary conditions applied to each beam elements are read and memorized in the structural variables;
- MAT_Stiffness_Matrix.f90: contains subroutines STIFFNESS_MATRIX, both for truss and Euler beam finite elements, in which the element stiffness matrix is computed in the local reference frame, then converted to the global reference frame and finally assembled in the global stiffness matrix;
- MAT_Load_Vector.f90: contains subroutines LOAD_VECTOR, both for truss and Euler beam finite elements, in which the nodal forces, the nodal torque, and distributed loads are eventually computed and applied by assembling the global forces vector adopting the same assembling procedure defined for the stiffness matrix;
- MAT_BC.f90: contains subroutines BC_ROUTINE, both for truss and Euler beam finite elements, in which the geometrical boundary conditions are applied to the structures by removing the rows/columns of the global finite element stiffness matrix and forces vector. In this subroutine, only pinned/hinged/clamped boundary conditions can be applied;
- SYS_LinearSystem.f90: contains subroutine LIN_SYS_LU, in which an elementary Gaussian back forward elimination algorithm is implemented for the computation of the solution of the final system of equations;
- POST_Postprocessor.f90: contains subroutines POSTPROCESSING, both for truss and Euler beam finite elements, in which the results are printed to screen and files, by printing element by element and node by node, the displacement components obtained;
Before starting, create in the directory where the code is compiled, two new folders "INPUT" and "RESULTS". Inside the /INPUT folder the following files related to the geometry, list node, cross-section and material properties and boundary conditions have to be created:
- NODES_LIST.dat: in this file, first the total number of nodes to define must be declared, and then in an ordered way one defines:
| 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|
| NODE_ID | X_COORD | Y_COORD | FX | FY | MZ |
In the case of truss elements, the sixth column is not read since there is no rotational degree of freedom.
- BC_LIST.dat: in this file, first the total number of geometric boundary conditions to define must be declared, and then in an ordered way one defines. In this case, to prescribe a constraint, the number "0" must be used to constraint that DOF, and the number "1" to let the DOF be free
| 1 | 2 | 3 | 4 |
|---|---|---|---|
| NODE_TO_APPLY_BC | X_DISP | Y_DISP | ROT_DISP |
In the case of truss elements, the fourth column is not read since there is no rotational degree of freedom.
- CONNECTIVITY.dat: in this file, in the first line the total number of finite elements to define and the element type (1 for truss, 2 for Bernoulli beam) must be declared, and then in an ordered way one defines:
| 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|
| ELE_ID | FIRST_NODE | SECOND_NODE | YOUNG | AREA | J_Y |
In the case of truss elements, the sixth column is not read since there is no rotational degree of freedom.