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Within the scheduling of construction projects, different, partly conflicting objectives have to be considered. The specification of an efficient construction schedule is a challenging task, which leads to a NP-hard multi-criteria optimization problem. In the past decades, so-called metaheuristics have been developed for scheduling problems to find near-optimal solutions in reasonable time. This paper presents a Simulated Annealing concept to determine near-optimal construction schedules. Simulated Annealing is a well-known metaheuristic optimization approach for solving complex combinatorial problems. To enable dealing with several optimization objectives the Pareto optimization concept is applied. Thus, the optimization result is a set of Pareto-optimal schedules, which can be analyzed for selecting exactly one practicable and reasonable schedule. A flexible constraint-based simulation approach is used to generate possible neighboring solutions very quickly during the optimization process. The essential aspects of the developed Pareto Simulated Annealing concept are presented in detail.
Solid behavior as well as liquid behavior characterizes the flow of granular material in silos. The presented model is based on an appropriate interaction of a displacement field and a velocity field. The constitutive equations and the applied algorithm are developed from the exact solution for a standard case. The standard case evolves from a very tall vertical plane strain silo containing material that flows at a constant speed. No horizontal displacements and velocities take place. No changes regarding the field values arise in the vertical direction and in time. Tension is not allowed at any point. Coulomb friction represents the effects of the vertical walls. The interaction between the flowing material and the walls is covered by a forced boundary condition resulting in an additional matrix for the solid component as well as for the liquid component. The resulting integral equations are designed to be solved directly. Three coefficients describe the properties of the granular material. They govern elastic solid behavior in combination with viscous liquid behavior.
Ausgehend von den fundierten Erfahrungen, die für das Schweißen von verschiedensten Metallen vorliegen, wird an der Professur Stahlbau der Bauhaus-Universität Weimar ein neuartiges Verfahren zum CO2-Laserstrahlschweißen von Quarzglas numerisch untersucht. Dabei kommt die kommerzielle FE-Software SYSWELD® zum Einsatz. Die erforderlichen Versuche werden in Zusammenarbeit mit dem Institut für Fügetechnik und Werkstoffprüfung GmbH aus Jena realisiert. Die numerische Analyse wird eingesetzt, um geeignete Prozessparameter zu bestimmen und deren Auswirkungen auf die transienten thermischen und mechanischen Vorgänge, die während des Schweißvorgangs ablaufen abzubilden. Um die aus der Simulation erhaltenen Aussagen zu überprüfen, ist es erforderlich, das Berechnungsmodell mittels Daten aus Versuchsschweißungen zu kalibrieren. Dabei sind die verwendeten Materialmodelle sowie die der Simulation zugrunde gelegten Materialkennwerte zu validieren. Es stehen verschiedene rheologische Berechnungsmodelle zur Auswahl, die die viskosen Materialeigenschaften des Glases abbilden. Dabei werden die drei mechanischen Grundelemente, die HOOKEsche Feder, der NEWTONsche Dämpfungszylinder und das ST.-VENANT-Element miteinander kombiniert. Die Möglichkeit, thermische und mechanische Vorgänge innerhalb des Glases während des Schweißvorgangs und nach vollständiger Abkühlung, vorhersagen zu können, gestattet es den Schweißvorgang über eine Optimierung der Verfahrensparameter gezielt dahingehend zu beeinflussen, die Wirtschaftlichkeit des Schweißverfahrens zu verbessern, und ein zuverlässiges Schweißergebnis zu erhalten. Dabei können auch nur unter hohem experimentellen Aufwand durchführbare Versuche simuliert werden, um eine Vorhersage zu treffen, ob es zweckmäßig ist, den Versuch auch in der Praxis zu fahren. Dies führt zu einer Reduzierung des experimentellen Aufwandes und damit zu einer Verkürzung des Entwicklungszeitraumes für das angestrebte Verfahren.
Polymer modification of mortar and concrete is a widely used technique in order to improve their durability properties. Hitherto, the main application fields of such materials are repair and restoration of buildings. However, due to the constant increment of service life requirements and the cost efficiency, polymer modified concrete (PCC) is also used for construction purposes. Therefore, there is a demand for studying the mechanical properties of PCC and entitative differences compared to conventional concrete (CC). It is significant to investigate whether all the assumed hypotheses and existing analytical formulations about CC are also valid for PCC. In the present study, analytical models available in the literature are evaluated. These models are used for estimating mechanical properties of concrete. The investigated property in this study is the modulus of elasticity, which is estimated with respect to the value of compressive strength. One existing database was extended and adapted for polymer-modified concrete mixtures along with their experimentally measured mechanical properties. Based on the indexed data a comparison between model predictions and experiments was conducted by calculation of forecast errors.
Using a quaternionic reformulation of the electrical impedance equation, we consider a two-dimensional separable-variables conductivity function and, posing two different techniques, we obtain a special class of Vekua equation, whose general solution can be approach by virtue of Taylor series in formal powers, for which is possible to introduce an explicit Bers generating sequence.
RESEARCH OF DEFORMATION OF MULTILAYERED PLATES ON UNDEFORMABLE BASIS BY UNFLEXURAL SPECIFIED MODEL
(2006)
Stress-strain state (SSS) of multilayered plates on undeformable foundation is investigated. The settlement circuit of transverse loaded plate is formed by symmetrical attaching of a plate concerning a surface of contact to the foundation. The plate of the double thickness becomes bilateral symmetrically loaded concerning its median surface. It allows to model only unflexural deformation that reduces amount of unknown and the general order of differentiation of resolving system of the equations. The developed refined continual model takes into account deformations of transverse shear and transverse compression in high iterative approximation. Rigid contact between the foundation and a plate, and also shear without friction on a surface of contact of a plate with the foundation is considered. Calculations confirm efficiency of such approach, allowing to receive decisions which is qualitative and quantitatively close to three-dimensional solutions.
We propose a new approach to the numerical solution of quasi-static elastic-plastic problems based on the Moreau-Yosida theorem. After the time discretization, the problem is expressed as an energy minimization problem for unknown displacement and plastic strain fields. The dependency of the minimization functional on the displacement is smooth whereas the dependency on the plastic strain is non-smooth. Besides, there exists an explicit formula, how to calculate the plastic strain from a given displacement field. This allows us to reformulate the original problem as a minimization problem in the displacement only. Using the Moreau-Yosida theorem from the convex analysis, the minimization functional in the displacements turns out to be Frechet-differentiable, although the hidden dependency on the plastic strain is non-differentiable. The seconds derivative exists everywhere apart from the elastic-plastic interface dividing elastic and plastic zones of the continuum. This motivates to implement a Newton-like method, which converges super-linearly as can be observed in our numerical experiments.
In this paper we present rudiments of a higher dimensional analogue of the Szegö kernel method to compute 3D mappings from elementary domains onto the unit sphere. This is a formal construction which provides us with a good substitution of the classical conformal Riemann mapping. We give explicit numerical examples and discuss a comparison of the results with those obtained alternatively by the Bergman kernel method.
The theory of regular quaternionic functions of a reduced quaternionic variable is a 3-dimensional generalization of complex analysis. The Moisil-Theodorescu system (MTS) is a regularity condition for such functions depending on the radius vector r = ix+jy+kz seen as a reduced quaternionic variable. The analogues of the main theorems of complex analysis for the MTS in quaternion forms are established: Cauchy, Cauchy integral formula, Taylor and Laurent series, approximation theorems and Cauchy type integral properties. The analogues of positive powers (inner spherical monogenics) are investigated: the set of recurrence formulas between the inner spherical monogenics and the explicit formulas are established. Some applications of the regular function in the elasticity theory and hydrodynamics are given.
New foundations for geometric algebra are proposed based upon the existing isomorphisms between geometric and matrix algebras. Each geometric algebra always has a faithful real matrix representation with a periodicity of 8. On the other hand, each matrix algebra is always embedded in a geometric algebra of a convenient dimension. The geometric product is also isomorphic to the matrix product, and many vector transformations such as rotations, axial symmetries and Lorentz transformations can be written in a form isomorphic to a similarity transformation of matrices. We collect the idea that Dirac applied to develop the relativistic electron equation when he took a basis of matrices for the geometric algebra instead of a basis of geometric vectors. Of course, this way of understanding the geometric algebra requires new definitions: the geometric vector space is defined as the algebraic subspace that generates the rest of the matrix algebra by addition and multiplication; isometries are simply defined as the similarity transformations of matrices as shown above, and finally the norm of any element of the geometric algebra is defined as the nth root of the determinant of its representative matrix of order n×n. The main idea of this proposal is an arithmetic point of view consisting of reversing the roles of matrix and geometric algebras in the sense that geometric algebra is a way of accessing, working and understanding the most fundamental conception of matrix algebra as the algebra of transformations of multilinear quantities.