Nama : Annie Wulandari MKPT Program Studi : Teknik Sipil Jurusan : Teknik Sipil Fakultas : Teknik Jenis Pekerjaan : Karya. Dengan hak noneksklusif ini secara cuma-cuma Universitas Indonesia berhak menyimpan, memindahkan/memformat, mengelola dalam bentuk database, memelihara dan menerbitkan skripsi saya selama tetap mencantumkan nama saya sebagai penulis/pencipta. dan sebagai pemilik hak cipta. Efek ukuran pada kekuatan struktural biasanya dipahami sebagai efek ukuran karakteristik struktur pada kekuatan nominal struktur ketika struktur yang mirip secara geometris dibandingkan.
The question is whether we can reproduce the size effect in modern numerical techniques. The results show that the use of a regularization method is necessary to produce a size effect.
INTRODUCTION
An analytical study of the size effect due to the localization of distributed cracks began in 19764. The second model is the three-point bending test, where a beam is considered to be imposed by a single load at the center of the beam. At the end of the chapter, the numerical result will be compared with the experimental result done by SYED Yasir Alam (2009).
Second, the crack is constrained to follow a predetermined path along the edges of the element, which casts doubt on the fidelity of the approach. Only the stress resultants and the accumulated strain over the cross section of the characteristic volume do. According to the above reasoning, one should not attempt to divide the width of the front of the crack band into several finite elements.
1. Matching between the softening curve of the cohesive crack model (a) and the stress-strain curve of the crack band model (b). From the point of view of the properties of the crack band model, the characteristic size lch can be obtained as Comparison of the distribution of axial displacements in the bar for the cohesive crack model (a, b) and the crack band model (c, d).
This is close to saying that the crack bandwidth hc is arbitrary, as it is replaced by the size of the element h(e) without appreciable effect (as long as the element size is kept small). This is easily implemented in a finite element program, regardless of the direction of the crack relative to the mesh lines11. Therefore, an approach is needed to overcome this sensitivity of the numerical result.
Adaptation of the softening law with respect to hc so that the dissipated energy is independent of the size of the finite elements11 2. On the other hand, if the structure is very small, the triangular stress relief zones have a negligible area compared to the area of the crack band, which means that the energy release is proportional to Mazars' damage model does not allow for the phenomenon of re-closure of the cracks (restoration of stiffness).
This model requires three material parameters: the value of ft, Gf and the shape of the σ(w) curve (the damping behavior). The first part of the fracture energy corresponds to the elastic contribution where damage has not yet occurred, i.e. d = 1.
NUMERICAL ANALYSIS
The right side of the bar is considered free where the increased uniaxial load is applied. At the center of the bar (area h, shown in Figure 4.1.1), the weakness is adjusted by reducing the tensile strength value ft. The global result of the force-displacement curves obtained for the four types of mesh thinning (Figure 4.1. 1) shows that there is clearly mesh independence when we change the size of the elements.
In terms of local behavior, as shown in Figure 4.1.2, grid independence also emerges. This model requires three material parameters: Gf, ft, and the shape of the σ(w) curve (softening behavior), which are considered material parameters independent of structural geometry and size. Thus, there will be an adjustment with respect to h, since h is considered a material property and is independent of the size of the finite element.
By applying the Hillerborg approach to the Mazars damage law, as mentioned in equation 3.3.26, the parameters of the Mazars model such as Bt and At can be obtained, since these parameters are the ones that affect the shape of the σ(w) curve. However, note that the stress parameters (Bt) in the Mazar damage model give influences on the peak load value. As shown in Figure 4.1.4 and Figure 4.1.5, the Hillerborg approach using the evolution damage law is able to give the same global result for any different network type.
This approach uses a localization limiter that enforces a specific size of an inelastic deformation region that is independent of the mesh refinement. This inability leads to a situation where the size of localization is independent of the size of the element. The result shows that in any type of mesh refinements it gives almost the same value of peak load and almost the same shape of the curve.
Meanwhile, for the local result, which is represented by the damage field in Figure 4.1.12, it satisfies the independence of the mesh refinement. The beams are subjected to a concentrated vertical load F at the center of the beam, and it is supported at the lower end of the beam. For reasons of simplicity, only half of the beam will be modeled as shown in Figure 4.2.1.
In addition to the global result, it is also necessary to look at the local result that the crack opening displacement (COD) can give, since the crack is one of the essential parameters for studying the strength behavior of the structure. . As previously mentioned, the damage parameters were calibrated by considering COD, so another value is needed to verify the accuracy of the calibration.
CONCLUSION
Therefore, La Borderie's law can give a good mesh independence result globally, but not in the local result. Another approach to overcome mesh dependency is to use a non-local method, by implementing a localization delimiter. The idea of this approach is to address the problem of predicting the position and number of the crack.
When the local behavior is observed, the calculation is shown to be mesh-independent. Therefore, the random property method is able to give a mesh - independent result globally and locally. The beam is pin-and-roll supported on the lower part of the beam and it is subjected to a concentrated load (–y direction) at the center of the beam.
There are three types of dimensions of the beam to be analyzed, D1, D2 and D3, to simulate the size effect of the structures. Calculation is done using Mazars Damage Law, therefore a notch is given in the bottom center as the damage law needs a point for a crack to form. The force-displacement curves vary for each type of beam as the size effect occurs, but the results obtained are not comparable to the experimental result as the damage law parameters used are different.
For local behavior, cracks appear along the mesh along the symmetry line according to the mesh refinement. The non-local Mazars damage parameters given are calibrated based on the experimental results of SYED Yasir Alam (2009). The force-displacement curves given by each type of beam simulate the size effect, so for the global result, the size effect can be simulated by regularization of numerical methods.
For the local behavior, crack length and crack opening are measured and compared with the test result. Given in Tables 4.2.3 and 4.2.4, the numerical results are overestimated compared to the experimental result, where relative errors that occur should be taken into account. However, the numerical results are calculated using displacement jumps, therefore a different approach to calculate the crack opening displacement to obtain a more accurate value comparable to the experimental results.
