Constrained form-finding results in a nonlinear system of equations unless a linear form-finding method (force density method) is iteratively applied until the given constraints are satisfied. ...Because the goal of this paper is to contribute to the further development of this method, a brief overview of the method and its existing improvements is provided. Further improvement can be potentially expected by reducing the number of iteration steps in solving systems of linear equations in each application of the force density method. To explore this, a comparison of iterative linear solvers is conducted. The Iterated Ritz method, as a new promising solver (currently under development), was chosen for comparison with typically used conjugate gradients. Form-finding of several truss structures in both tension and compression was performed to compare the number of iteration steps necessary to obtain the solution. The presented form-finding examples indicated a significant reduction in the number of solver iteration steps, showing the potential of the Iterated Ritz method for use as a solver in linear procedures for constrained form-finding.
Constrained form-finding; Iterated force density method; Conjugate gradient method; Iterated Ritz method; Cable net; Gridshell
This research was carried out to develop a novel composite material consisting of a thread reinforcement and a clay matrix, as well as to develop a method of shaping this material into hollow spatial ...structures. Ceramic elements in the building industry are currently created by applying extruding, pressing and casting methods. The approach of spraying clay onto predefined knitted meshes increases the usability of digitally fabricated lightweight ceramic elements, while eliminating the need for scaffolding. In this approach, multiple layers of a fluid clay mass are sprayed onto the tensioned mesh using an industrial, six-axis robotic arm. This allows the precise application of the material and results in varying material thicknesses. Due to the complementary qualities of clay which absorbs compressive forces and threads which absorb tensile forces, lightweight structures can be created. The research involved experimenting with clay mixtures, several thread types, knitting methods and spraying techniques, as well as fabricating a 1:1 lightweight module as an architectural prototype.
In this paper some basic physical and mechanical properties of glass as structural material are presented. This research is about specifically manufactured glass railing element that will be a part ...of a pedestrian bridge construction in Zagreb, Croatia. Load bearing capacity test of the glass railing element is conducted within the Faculty of Civil Engineering in Zagreb and obtained experimental results are discussed and compared to the ones provided by the numerical model. Taking into account the behaviour of laminated glass and results of experimental and numerical testing, glass railing element can be regarded as safe.
In Structural Analysis 2, the third year’s course of undergraduate studies at the Faculty of Civil Engineering, University of Zagreb, students acquire theoretical knowledge on the design of tensile ...structures (with emphasis on prestressed cable nets). Prior to calculation, to better understand the problem of form finding, students are assigned to build a physical model of tensile structure from elastic mesh fabric. Following, they apply the force density method to numerically determine the equilibrium position. To establish numerical model, Rhinoceros and Grasshopper (visual programming language within Rhinoceros) are used, while calculations are made in SageMath, an open-source mathematical software.
godina usvajaju teorijsko znanje o oblikovanju vlačnih prednapetih konstrukcija (s naglaskom na mreže prednapetih kabela). Radi boljega razumijevanja problema traženja oblika, a primjereno ...preddiplomskom studiju, studenti su kolegija akademske godine 2019./2020. izrađivali fizički model vlačne konstrukcije od elastične mrežaste tkanine. Potom su primjenom metode gustoća sila numerički definirali ravnotežni položaj primjenom programa Rhinoceros i Grasshopper (vizualni programski jezik i okruženje u Rhinocerosu 3D) te SageMath.
The method for reducing total computational time during iterative application of the force density method, intended to attain prescribed force values in cables or prescribed lengths of cable ...segments, is described in the paper. In each step of the iterative procedure, linear systems are solved with the accuracy that takes into account differences between the calculated and required values. The rule that prevents excessively fast increase in accuracy, while maintaining it high enough not to compromise the convergence of the iterative process, is proposed.
U radu je opisan postupak skraćivanja trajanja proračuna pri iteracijskoj primjeni metode gustoća sila kojom se u fazi nalaženja oblika prednapete konstrukcije od užadi postižu tražene vrijednosti ...sila ili duljine odsječaka kabela. U svakom se iteracijskom koraku linearni sustavi jednadžbi rješavaju s točnošću koja u obzir uzima razlike izračunanih i traženih vrijednosti. Predloženo je pravilo koje sprečava prebrzo povećavanje točnosti, održavajući je istodobno dovoljno velikom da se konvergencija ne naruši.
Familija ploha Heltocat Kodrnja, Iva; Šamec, Elizabeta
KoG,
01/2016, Letnik:
19., Številka:
19.
Paper
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U radu je prema 5 denirana familija ploha Heltocat. Za plohe iz definirane familije se pokazuje da su minimalne i da čine izometričnu deformaciju od helikoida do katenoida. Za vizualizaciju ploha i ...račune su korišteni programi Sage i Mathematica.
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