Here, I present a simple code to solve the structural analysis using the PARDISO package.
Periodic boundary conditions are activated by initializing the variable pphase(1:9). Then, specify the constraint: This is done by the vector pphase(/s(1),s(2),s(3),s(4),s(5),s(6),s(7),s(8),s(9)/). The parameters s(1) to s(9) can be initialized with .TRUE. or .FALSE. depending on whether the constrains s(i) is active. s(1) - constrain x=0 in x; s(2) - constrain x=0 in y; s(3) -constrain x=0 in z; s(4) - constrain y=0 in x; etc.
The pphase variable appears in the input file, mesh_analysis_CSR_3Dx3_sym.f90, structural_3D.f90,
- read input file (LA,LB,na,nb)
- run symbolic mesh analysis to obtain: IA, JA, TFEM_CSR, K_diag
- assembly the stiffness matrix K (consider parallelization)
- provide the nodal force F and boundary conditions using the penalty method
- solve K u = F using PARDISO (consider parallelization)
- postprocess results (displacement field) u
It is assumed that the numbering of nodes, elements and degrees of freedom is such as shown in the figure below:
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2D:
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3D:
The red node is the node which connets all eight elements togehter. Each node contains three degrees of freedom u_x, u_y, and u_z.