The Dynamic Analysis of Structures by Boundary Element Method Project stands as an advanced computational tool tailored for the dynamic analysis of plane scalar time-domain challenges over an isotropic half-space. The detailed flowchart in figure below, outlines the functionality of The DASBEM Project for seismic analysis of subsurface inclusions. This numerical procedure is seamlessly executed through the MATLAB programming software.

• INPUT DATA: Retrieve input from the file generated by the WRITE DATA sub-problem. This includes shear wave velocity, number of time steps, number and coordinates of boundary nodes, their boundary conditions, number of internal points, and any existing loading data.

• COMPUTE GHMAT: Calculate the elements of matrices G and H using numerical integration.

• NONSING: Determine the non-singular elements of the aforementioned matrices.

• SING: Identify the singular elements of matrix G using specialized numerical integration.

• FUNSOLE: Incorporate elastodynamic fundamental solutions for half-plane conditions, utilized by NONSING and SING during numerical integration.

• HDIAG: Compute the diagonal elements of matrix H.

• COMPUTE GHARG: Assemble the matrices computed in previous steps.

• COMPUTE AFMAT: Formulate the solvable equations based on boundary conditions at each node.

• FUNCVAL: This sub-program is invoked by COMPUTE AFMAT when loading is in the form of external vibrations.

• COMPUTE UTMAT: Establish the boundary conditions for u and q.

• COMPUTE PREST: Incorporate historical dynamic time data and call for the current free-field motion boundary.

• COMPUTE INTP: Calculate responses at internal points.

• OUTPUT DATA: Output responses from boundary nodes and internal points.

Step-by-step guide to using The DASBAM Project

🔸 WRITE_DATA

• Open WRITE_DATA and set the following values: a) Shear modulus of the domain and inclusion (assumed values: '16e5' and '3.24e5', respectively). b) Density of the domain and inclusion (assumed values: '1' and '0.6667', respectively). c) Number of time steps and time increments (assumed values: '400' and '0.0175', respectively). d) Radius (b) and depth (D) of the inclusion (assumed values: '500' and '750', respectively). e) Shape of the inclusion (assumed shape: circular). f) Size of half-element (assumed value: '30'). g) Predominant frequency (assumed value: '3'). h) Time shift parameter (assumed value: '2.4'). i) Angle of incident wave (assumed angle: '0'). j) Range of ground surface "internal points" (assumed value: '-3b to 3b').

🔸 MAIN_PROGRAM

• Open MAIN_PROGRAM and execute it. Wait until the calculations are complete.

🔸 CONVERGENCE_DIAGRAM

• Refer to CONVERGENCE_DIAGRAM to determine if convergence in responses has been achieved.

🔸 FFT

• Use FFT to display the 2D normalized displacement amplitude (NDA) of the surface.

🔸 DIAGRAM_3D

• Use DIAGRAM_3D to visualize the 3D time and frequency domain responses.

Some computed results from The DASBAM Project for a subsurface inclusion

Panji, M., Mojtabazadeh-Hasanlouei, S. and Yasemi, F. (2020). "A half-plane time-domain BEM for SH-wave scattering by a subsurface inclusion", Computers & Geosciences, 134, 1-19. DOI: 10.1016/j.cageo.2019.104342

⚠️ Utilizing The DASBAM Project with proper attribution is permitted ⚠️

• www.drmojtabazadeh.ir
• www.saeed-mojtabazadeh.ir