From Laser Scanning to Finite Element Analysis of Complex Buildings by Using a Semi-Automatic Procedure

Abstract

In this paper, a new semi-automatic procedure to transform three-dimensional point clouds of complex objects to three-dimensional finite element models is presented and validated. The procedure conceives of the point cloud as a stacking of point sections. The complexity of the clouds is arbitrary, since the procedure is designed for terrestrial laser scanner surveys applied to buildings with irregular geometry, such as historical buildings. The procedure aims at solving the problems connected to the generation of finite element models of these complex structures by constructing a fine discretized geometry with a reduced amount of time and ready to be used with structural analysis. If the starting clouds represent the inner and outer surfaces of the structure, the resulting finite element model will accurately capture the whole three-dimensional structure, producing a complex solid made by voxel elements. A comparison analysis with a CAD-based model is carried out on a historical building damaged by a seismic event. The results indicate that the proposed procedure is effective and obtains comparable models in a shorter time, with an increased level of automation.

Keywords: cultural heritage; finite element analysis; geometric modeling; historical buildings; structural analysis; terrestrial laser scanning.

Figure 1

Flowchart for the proposed method: completely automated procedures (green) and semi-automated or manual procedures (orange).

Figure 2

Visualization of the stacking layer sequence concept. (a) Point cloud survey of external façades; (b) point cloud survey of internal surfaces; (c) illustration of the m-th slice; (d) ${\text{Π}}_j^z$ layer.

Figure 3

Two dimensional images obtained by slicing the structure illustrated in Figure 2: m, n and r represent three generic slices located at the z_m, z_n and z_r coordinates respectively. (a) ${\text{Π}}_m^z$; (b) ${\text{Π}}_n^z$; (c) ${\text{Π}}_r^z$.

Figure 4

Voxel representation and finite element transformation: {i, j, k} and {X, Y, Z} are the indexes of the voxels’ three-dimensional matrix and the global coordinates of the structure, respectively. The coordinate k' means k' = R − k, where Ris the third size (along Z) of the voxels’ three-dimensional matrix (N × M × R). (a) Voxel indexes;(b) hexahedral elements.

Figure 5

Finite element mesh obtained by applying the procedure to the structure represented in Figure 2. (a) External restitution; (b) internal restitution; (c) smoothed internal restitution.

Figure 6

San Felice sul Panaro Fortress principal tower. (a) South front; (b) east front; (c) E-W section; (d) S-N section.

Figure 7

Three-dimensional models for Mastio tower. (a) Points; (b) triangular irregular network (TIN) mesh.

Figure 8

First part of the slicing workflow (3D data): the magnified portion shows the uneven density of the raw data. (a) Points within the Δz increment; (b) final processed slice of points.

Figure 9

Second part of the slicing workflow (2D data). (a) Internal (red), external (green); (b) filled slice; (c) bitmap: 116 × 107 pixels.

Figure 10

Examples of bitmap slices. (a) 42nd slice; (b) 84th slice; (c) 128th slice.

Figure 11

Visualization of the three-dimensional material matrix: voxels possess unitary dimension. Five materials (colors) are used to represent the structure according to the mechanical characterization given in Table 1.

Figure 12

Finite element discretization comparison; colors are set according to the material properties: gray and red colors are used to illustrate the masonry and the reinforced masonry elements, respectively. (a) CLOUD2FEM discretization; (b) CAD-based discretization.

Figure 13

Mode 1: bending mode shape. Displacements magnitude. (a) Voxel frequency = 1.9131 Hz; (b) CAD frequency = 1.9137 Hz.