| 1. |
- Christensen, P. W., et al.
(författare)
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Formulation and comparison of algorithms for frictional contact problems
- 1998
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 42:1, s. 145-173
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents two algorithms for solving the discrete, quasi-static, small-displacement, linear elastic, contact problem with Coulomb friction. The algorithms are adoptions of a Newton method for solving B-differentiable equations and an interior point method for solving smooth, constrained equations. For the application of the former method, the contact problem is formulated as a system of B-differentiable equations involving the projection operator onto sets with simple structure; for the application of the latter method, the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non-negativity of variables treated as constraints. The two algorithms are numerically tested for two-dimensional problems containing up to 100 contact nodes and up to 100 time increments. Results show that at the present stage of development, the Newton method is superior both in robustness and speed. Additional comparison is made with a commercial finite element code.
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| 2. |
- Kjellmert, Bo
(författare)
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A Chebyshev collocation multidomain method to solve the Reissner-Mindlin equations for the transient response of an anisotropic plate subjected to impact
- 1997
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Ingår i: International Journal for Numerical Methods in Engineering. - 0029-5981 .- 1097-0207. ; 40:20, s. 3689-3702
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Tidskriftsartikel (refereegranskat)abstract
- The transient response of an anisotropic rectangular plate subjected to impact is described through a Chebyshev collocation multidomain discretization of the Reissner-Mindlin plate equations. The trapezoidal rule is used for time-integration. The spatial collocation derivative operators are represented by matrices, and the subdomains are patched by natural and essential conditions. At each time level the resulting governing matrix equation is reduced by two consecutive block Gaussian eliminations, so that an equation for the variables at the subdomain corners has to be solved. Back-substitution gives the variables at all other collocation points. The time history as represented by computed contour plots has been compared with analytical results and with photos produced by holographic interferometry. The agreements are satisfactory.
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| 3. |
- Kjellmert, Bo
(författare)
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A spectral method to solve the equations of linear elasticity for the transient response of a tube subjected to impact
- 1999
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Ingår i: International Journal for Numerical Methods in Engineering. - 0029-5981 .- 1097-0207. ; 45:8, s. 1115-1133
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Tidskriftsartikel (refereegranskat)abstract
- The transient response of a tube subjected to impact is described through Fourier-Galerkin and Chebyshev collocation multidomain discretizations of the equations of linear elasticity. The trapezoidal rule is used for time integration. For each Fourier mode the spatial collocation derivative operators are represented by matrices, and the subdomains are patched by natural and essential conditions. At each time level the resulting governing matrix equation is reduced by two consecutive block Gaussian eliminations, so that an equation for the complex Fourier coefficients at die subdomain corners has to be solved. Back-substitution gives the coefficients at all other collocation points. An inverse discrete Fourier transform generates, at optional time levels, the three components of the displacement field. Through this method the long-term evolution of the field may be calculated, provided the impact time is long enough. The time history as represented by computed contour plots has been compared with photos produced by holographic interferometry. The agreements are satisfactory.
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| 4. |
- Lindgren, Lars-Erik, et al.
(författare)
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Simulation of multipass welding of a thick plate
- 1999
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Ingår i: International Journal for Numerical Methods in Engineering. - 0029-5981 .- 1097-0207. ; 44:9, s. 1301-1316
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Tidskriftsartikel (refereegranskat)abstract
- Multipass butt welding of a very thick steel plate has been performed. Transient temperatures and residual stresses have been measured. The agreement between calculations and experiments is good. Two different approaches, quiet and inactive elements, for modelling multipass welding are compared. The first approach is straightforward to apply in most finite element codes. The inactive element method requires a code that can regenerate the finite element model automatically or otherwise very tedious manual work is necessary as the elements are added to the model when welds are laid. It is shown that both techniques give the same results but the computational effort is reduced by using inactive elements. It also circumvents the problem in the quiet element approach of choosing properties of elements in the model that represent the case when welds are not laid.
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| 5. |
- Svoboda, Ales, et al.
(författare)
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The effective stress function algorithm for pressure‐dependent plasticity applied to hot isostatic pressing
- 1998
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Ingår i: International Journal for Numerical Methods in Engineering. - 0029-5981 .- 1097-0207. ; 43:4, s. 587-606
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Tidskriftsartikel (refereegranskat)abstract
- An algorithm for unconditionally stable and accurate integration of elasto-viscoplastic pressure-dependent constitutive model is presented. Rate form constitutive equations of thermal-elastoviscoplastic type with compressibility take into account the changes in relative density. The algorithm computes the deviatoric and volumetric creep strains by finding the value of the effective stress which satisfies the functional relationship, the effective stress function. Thus, one non-linear scalar equation is solved to find the unknown volumetric and deviatoric components of creep strain tensor. The tangent modulus is evaluated consistent with the integration algorithm. The application of the method to the simulation of hot isostatic pressing of metal powder is shown. The paper presents the solution of the verification problem and comparison with the experimental result.
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| 6. |
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| 7. |
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| 8. |
- Alastrue, V., et al.
(författare)
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On the use of non-linear transformations for the evaluation of anisotropic rotationally symmetric directional integrals. Application to the stress analysis in fibred soft tissues
- 2009
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 1097-0207 .- 0029-5981. ; 79:4, s. 474-504
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Tidskriftsartikel (refereegranskat)abstract
- Microsphere-based constitutive models are a helpful tool in the modelling of materials with a microstructure composed of contributing elements directionally arranged. This is the case, for instance, for fibred soft tissues. In these models, the macroscopic mechanical behaviour is obtained from the integration of the micro-structural contribution of each component (e.g. each fibre) over the surface of an underlying microsphere, which allows incorporating the mechanical features of the micro-constituents to the macroscopic response. The combination of this sort of models and the associated numerical techniques constitutes a powerful modelling tool for which an efficient integration scheme is required. In this regard, the unit sphere discretizations proposed by Bazant and Oh (ZAMM-J Appl Math Mech Z Angew Math Mech 1986; 66(1):37-49) have been used for the integration of the microscopic contributions in isotropic materials. Nevertheless, the inclusion of anisotropy has important implications with regard to the integration scheme, since very fine discretizations are needed to perform the integration accurately, causing the integration process to be very costly. In addition, the storage of internal variables at each integration direction of every integration point is required for constitutive models based on the use of internal variables at the micro-structural level, which renders this approach rather complex and memory demanding. In order to reduce the number of necessary integration directions, several non-linear transformations for the integration of rotationally symmetric functions over the Surface of the unit sphere are here presented. Their accuracy in the integration of the von Mises orientation distribution function is evaluated. Furthermore, a hyperelastic microsphere-based constitutive law for the modelling of soft biological tissues is used in order to check the accuracy and computational efficiency of the proposed transformations within a Finite Element context in inhomogeneous deformation problems. Simulation results show the suitability of the proposed methodology in order to accurately approximate the Value of the integrals within reasonable computational costs. Copyright (C) 2009 John Wiley & Sons, Ltd.
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| 9. |
- Appelo, D., et al.
(författare)
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An energy-based discontinuous Galerkin method for coupled elasto-acoustic wave equations in second-order form
- 2019
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 119:7, s. 618-638
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Tidskriftsartikel (refereegranskat)abstract
- We consider wave propagation in a coupled fluid-solid region separated by a static but possibly curved interface. The wave propagation is modeled by the acoustic wave equation in terms of a velocity potential in the fluid, and the elastic wave equation for the displacement in the solid. At the fluid solid interface, we impose suitable interface conditions to couple the two equations. We use a recently developed energy-based discontinuous Galerkin method to discretize the governing equations in space. Both energy conserving and upwind numerical fluxes are derived to impose the interface conditions. The highlights of the developed scheme include provable energy stability and high order accuracy. We present numerical experiments to illustrate the accuracy property and robustness of the developed scheme.
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| 10. |
- Araujo-Cabarcas, Juan Carlos, 1981-, et al.
(författare)
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Shape optimization for the strong directional scattering of dielectric nanorods
- 2021
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Ingår i: International Journal for Numerical Methods in Engineering. - : John Wiley & Sons. - 0029-5981 .- 1097-0207. ; 122:8, s. 3683-3704
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Tidskriftsartikel (refereegranskat)abstract
- In this project, we consider the shape optimization of a dielectric scatterer aiming at efficient directional routing of light. In the studied setting, light interacts with a penetrable scatterer with dimension comparable to the wavelength of an incoming planar wave. The design objective is to maximize the scattering efficiency inside a target angle window. For this, a Helmholtz problem with a piecewise constant refractive index medium models the wave propagation, and an accurate Dirichlet-to-Neumann map models an exterior domain. The strategy consists of using a high-order finite element (FE) discretization combined with gradient-based numerical optimization. The latter consists of a quasi-Newton (BFGS) with backtracking line search. A discrete adjoint method is used to compute the sensitivities with respect to the design variables. Particularly, for the FE representation of the curved shape, we use a bilinear transfinite interpolation formula, which admits explicit differentiation with respect to the design variables. We exploit this fact and show in detail how sensitivities are obtained in the discrete setting. We test our strategy for a variety of target angles, different wave frequencies, and refractive indexes. In all cases, we efficiently reach designs featuring high scattering efficiencies that satisfy the required criteria.
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