Numerical Methods for the Simulation of Deformations and Stresses in Turbine Blade Fir-Tree Connections

Benad, Justus

doi:10.22190/fume190103008b

Cited by 8 publications

(8 citation statements)

References 29 publications

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“…Turbine blades and discs are among these critical components [7,8]. Highly undulating surfaces, cooling holes, and other complex geometrical elements in close proximity to the contact regions of turbine blade fir-tree connections cause difficulties when using the half-space theory to model deformations and stresses [9]. Therefore, other modeling techniques have to be used for these kinds of problems, such as the Finite Element Method (FEM) or the classical BEM for arbitrary shapes [10].…”

Section: Introductionmentioning

confidence: 99%

Efficient Calculation of the Bem Integrals on Arbitrary Shapes With the FFT

Benad

2018

FU Mech Eng

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This paper builds upon the results of a recent study which illustrates how the Fast Fourier Transformation (FFT) can be used to accelerate the Boundary Element Method (BEM) for arbitrary shapes. In the present work, we further deepen this understanding and focus especially on implementation details in order to calculate the boundary integrals with the FFT. Different numerical techniques are compared for an exemplary shape. Also, additions to the concept are mentioned such as the introduction of a high-resolution grid close to the boundary and a low-resolution grid farther away.

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Section: Introductionmentioning

confidence: 99%

Efficient Calculation of the Bem Integrals on Arbitrary Shapes With the FFT

Benad

2018

FU Mech Eng

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“…Recently, the fast Fourier transform method has been incorporated with the boundary-element method for solving problems with an arbitrary columnar geometry, not confined by the half-space assumption (Benad, 2018(Benad, , 2019. This further extends the breadth of FFT applications.…”

Section: Range Of Applications Of the Fft Approachesmentioning

confidence: 99%

“…This further extends the breadth of FFT applications. For the plane-strain problems associated with a columnar geometry formed by extruding a 2D shape in the length direction, e.g., the one solved by Benad (2018Benad ( , 2019, the FFT solutions have a lower computational complexity, O(n 3 log n 1.5 ), than the inversion of a standard BEM matrix, O(n 4 ), where n x n is the total number of surface nodes. These problems are, mathematically, in the same nature as that in Figure 2F, automatically meeting the DC-FFT requirement with no need of the domain extension, as indicated in the first row of Table 1 and Figure 13.…”

Section: Range Of Applications Of the Fft Approachesmentioning

confidence: 99%

FFT-Based Methods for Computational Contact Mechanics

et al. 2020

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Computational contact mechanics seeks for numerical solutions to contact area, pressure, deformation, and stresses, as well as flash temperature, in response to the interaction of two bodies. The materials of the bodies may be homogeneous or inhomogeneous, isotropic or anisotropic, layered or functionally graded, elastic, elastoplastic, or viscoelastic, and the physical interactions may be subjected to a single field or multiple fields. The contact geometry can be cylindrical, point (circular or elliptical), or nominally flat-to-flat. With reasonable simplifications, the mathematical nature of the relationship between a surface excitation and a body response for an elastic contact problem is either in the form of a convolution or correlation, making it possible to formulate and solve the contact problem by means of an efficient Fourier-transform algorithm. Green's function inside such a convolution or correlation form is the fundamental solution to an elementary problem, and if explicitly available, it can be integrated over a region, or an element, to obtain influence coefficients (ICs). Either the problem itself or Green's functions/ICs can be transformed into a space-related frequency domain, via a Fourier transform algorithm, to formulate a frequency-domain solution for contact problems. This approach converts the original tedious integration operation into multiplication accompanied by Fourier and inverse Fourier transforms, and thus a great computational efficiency is achieved. The conversion between ICs and frequency-response functions facilitate the solutions to problems with no explicit space-domain Green's function. This paper summarizes different algorithms involving the fast Fourier transform (FFT), developed for different contact problems, error control, as well as solutions to the problems involving different contact geometries, different types of materials, and different physical issues. The related works suggest that (i) a proper FFT algorithm should be used for each of the cylindrical, point, and nominally flat-flat contact problems, and then (ii) the FFT-based algorithms are accurate and efficient. In most cases, the ICs from the 0order shape function can be applied to achieve satisfactory accuracy and efficiency if (i) is guaranteed.

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“…Relations ( 8) and ( 9) can be obtained from the fundamental solution of (1). For details see (Benad, 2019).…”

Section: Boundary Integral Formulationmentioning

confidence: 99%

“…The pFFT may provide an opportunity to accelerate Boundary Element calculations of contact problems with a more difficult geometry. An exemplary application may be turbine blade firtree connections, a contact problem where the half-space theory is pushed to its limits (Benad, 2019). Naturally, the pFFT approach is not restricted to geometries where the domain of interest is the inner region which is enclosed by the boundary.…”

Section: Introductionmentioning

confidence: 99%

Calculation of the BEM Integrals on a Variable Grid With the FFT

Benad

2020

Front. Mech. Eng.

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In this study, an exemplary application of the pFFT is shown for the 2D Navier equation for a linear elastic continuum. Using this example, it is illustrated how the pFFT might be extended in order to decrease the computational complexity of the method. In the standard pFFT approach, all panel influences which are not calculated directly are obtained using a single regular grid. In the present study, a variable gird is suggested to obtain these influences. It is outlined how it is possible to apply the FFT on each level of this variable grid by rearranging segments of the shape boundary. A brief example is presented which indicates feasibility of the concept.

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Numerical Methods for the Simulation of Deformations and Stresses in Turbine Blade Fir-Tree Connections

Cited by 8 publications

References 29 publications

Efficient Calculation of the Bem Integrals on Arbitrary Shapes With the FFT

Efficient Calculation of the Bem Integrals on Arbitrary Shapes With the FFT

FFT-Based Methods for Computational Contact Mechanics

Calculation of the BEM Integrals on a Variable Grid With the FFT

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