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Smart and adaptive outer façade shading systems are of high interest in modern architecture. For long lasting and reliable systems, the abandonment of hinges which often fail due to mechanical wear during repetitive use is of particular importance. Drawing inspiration from the hinge-less motion of the underwater snap-trap of the carnivorous waterwheel plant (Aldrovanda vesiculosa), the compliant façade shading device Flectofold was developed. Based on computational simulations of the biological role-model’s elastic and reversible motion, the actuation principle of the plant can be identified. The enclosed geometric motion principle is abstracted into a simplified curved-line folding geometry with distinct flexible hinge-zones. The kinematic behaviour is translated into a quantitative kinetic model, using finite element simulation which allows the detailed analyses of the influence of geometric parameters such as curved-fold line radius and various pneumatically driven actuation principles on the motion behaviour, stress concentrations within the hinge-zones, and actuation forces. The information regarding geometric relations and material gradients gained from those computational models are then used to develop novel material combinations for glass fibre reinforced plastics which enabled the fabrication of physical prototypes of the compliant façade shading device Flectofold.

We present a variational method for problems in solid and structural mechanics that is designed to be intrinsically free from locking when using equal order interpolation for all involved fields. The specific feature of the formulation is that it avoids all geometrical locking effects (as opposed to material locking effects, e.g. Poisson locking) for any type of structural or solid model, independent of the underlying discretization scheme. The possibility to employ equal order interpolation for all involved fields circumvents the task of finding particular function spaces to remove locking and avoid artificial stress oscillations. This is particularly attractive for instance for isogeometric analysis using unstructured meshes or T-splines. Comprehensive numerical tests underline the promising behaviour of the proposed method for geometrically linear and non-linear problems in terms of displacements and stress resultants using standard finite elements, isogeometric finite elements and a meshless method.

In this contribution, a novel local, node-based time step estimate for reciprocal mass matrices is proposed. Element-based estimates turn out to be not generally conservative and are consequently inadequate. Therefore, the nodal time step estimate for diagonally lumped mass matrices based on Gershgorin’s theorem is further developed for application to reciprocal mass matrices. Additionally, simplifications of the proposed time step estimate that improve computational efficiency, especially for contact problems with the penalty method, are discussed and evaluated by numerical examples.

The skeleton of Echinocyamus pusillus is considered as an exceptional model organism for structural strength and skeletal integrity within the echinoids as demonstrated by the absence of supportive collagenous fibres between single plates and the high preservation potential of their skeletons. The structural principles behind this remarkably stable, multi-plated, light-weight construction remain hardly explored. In this study, high-resolution X-ray micro-computed tomography, finite-element analysis and physical crushing tests are used to examine the structural mechanisms of this echinoid’s skeleton. The virtual model of E. pusillus shows that the material is heterogeneously distributed with high material accumulations in the internal buttress system and at the plate boundaries. Finite-element analysis indicates that the heterogeneous material distribution has no effect on the skeleton’s strength. This numerical approach also demonstrates that the internal buttress system is of high significance for the overall skeletal stability of this flattened echinoid. Results of the finite-element analyses with respect to the buttress importance were evaluated by physical crushing tests. These uniaxial compression experiments support the results of the simulation analysis. Additionally, the crushing tests demonstrate that organic tissues do not significantly contribute to the skeletal stability. The strength of the echinoid shell, hence, predominantly relies on the structural design.

The fast motion of the snap-traps of the terrestrial Venus flytrap (Dionaea muscipula) have been intensively studied, in contrast to the tenfold faster underwater snap-traps of its phylogenetic sister, the waterwheel plant (Aldrovanda vesiculosa). Based on biomechanical and functional–morphological analyses and on a reverse biomimetic approach via mechanical modelling and computer simulations, we identify a combination of hydraulic turgor change and the release of prestress stored in the trap as essential for actuation. Our study is the first to identify and analyse in detail the motion principle of Aldrovanda, which not only leads to a deepened understanding of fast plant movements in general, but also contributes to the question of how snap-traps may have evolved and also allows for the development of novel biomimetic compliant mechanisms.

In 2017, the University of Stuttgart started a Collaborative Research Centre with the title Adaptive Skins and Structures for the Built Environment of Tomorrow. The goal of this research project is to find an answer to today’s most urgent social and ecological questions as the global population continuously increases and the available resources remain limited. As the central approach to the solution of this problem, adaptive elements will be included in the structure, the interior and the façade of an experimental 37 m tall building. This paper introduces the topic of adaptivity in building structures and provides an overview of the research topics applied in this globally unique adaptive high-rise building. Due to the complexity of research topics of this Collaborative Research Centre, this paper only covers the research concerning the experimental high-rise building.

Adaptive structures in civil engineering are mechanical structures with the ability to modify their response to external loads. Actuators strongly affect a structure’s adaptivity and have to be placed thoughtfully in the design process to effectively compensate external loads. For constant loads, this property is introduced as steadystate disturbance compensability. This property can be linked to concepts from structural engineering such as redundancy or statical indeterminacy, thus representing an interdisciplinary approach. Based on the disturbance compensability matrix, a scalar performance metric is derived as quantitative measure of a structure’s ability to compensate the output error for arbitrary constant disturbances with a given set of actuators. By minimizing this metric, an actuator configuration is determined. The concept is applied to an example of a truss structure.

This contribution proposes a new approach to derive geometrically parameterized, reduced order finite element models. An element formulation for geometrically parameterized finite elements is suggested. The parameterized elements are used to derive models with a parameterized geometry where the parameterized system matrices are expressed in an affine representa- tion. Parametric model order reduction can then be efficiently used to reduce the full order parameterized model to a reduced order parameterized model. The approach shows two beneficial features. First, design studies and shape optimizations can be conducted with parameterized reduced order model of much lower dimension compared to the parameterized, full order model. Second, it is possible to compute sensitivities analytically, and therefore, to avoid the computation of finite differences gradients. The approach is illustrated with two numerical examples. The first example includes a detailed error analysis. The second example is a shape optimization example of an adaptive structure.

Angesichts einer stetig steigenden Anzahl komplexer Diskretisierungsverfahren beschäftigt sich die vorliegende Arbeit mit intrinsisch lockingfreien Schalenformulierungen. Aus der Literatur bekannte Konzepte versuchen stets die durch die Diskretisierung entstehenden Locking-Effekte zu beseitigen oder abzumindern. Tritt Locking jedoch gar nicht auf, ist dessen Beseitigung obsolet. Deshalb sollen die hier vorgestellten Schalenformulierungen numerische Locking-Effekte bereits auf Theorieebene vermeiden, ungeachtet vom verwendeten Diskretisierungsschema. Die Vermeidung von Locking bereits vor der Diskretisierung verspricht ein breites Anwendungsspektrum für diverse Diskretisierungsverfahren im Bereich von Computersimulationen physikalischer Vorgänge. Der erste Teil dieser Arbeit beschäftigt sich mit der intrinsischen Vermeidung von Querschublocking in Formulierungen für Strukturtheorien. Über hierarchische Reparametrisierung der kinematischen Gleichungen kann Querschublocking im Rahmen einer primalen Methode a priori vermieden werden. Das Konzept wird gleichermaßen für schubweiche Balken-, Platten- und Schalenformulierungen demonstriert, wobei jeweils zwei hierarchische Parametrisierungen unterschieden werden. Der zweite theoretische Teil dieser Arbeit beschäftigt sich mit der intrinsischen Vermeidung aller geometrischen Locking-Effekte, vor allem aber von Membranlocking. Es wird ein neuartiges, reparametrisiertes gemischtes Prinzip vorgestellt, in dem ausschließlich Verschiebungsgrößen als Primärvariablen auftreten. Diese Reparametrisierung führt dazu, dass die für gemischte Methoden notwendige Wahl geeigneter Spannungs- oder Verzerrungsräume entfällt. Die daraus resultierende intrinsische Vermeidung geometrischer Locking-Effekte verspricht ein breites Anwendungsspektrum dieser Methode.

In the context of isogeometric contact analysis, surfaces of objects can be described smoothly due to the high continuity of the involved shape functions. This facilitates construction of a continuous normal field which may be beneficial for modeling of contact problems. This property allows for stable collocation of the virtual contact work using considerable less evaluation points than numerical integration, while the approximation quality of the computational results is almost the same. In this context, a weighted point-based method (PTS+) is introduced as an extension of the Point-To-Segment method (PTS) proposed previously by Matzen et al. (2013). The weights enable transmission of contact stresses instead of contact forces along the contact surfaces. In normal direction the non-penetration condition is enforced by the Lagrange multiplier method, combined with the penalty method in tangential direction. Corresponding to the collocation weights, a constant or NURBS Lagrange multiplier field is introduced. A comparison between the collocation-based contact formulations PTS, PTS+ and a mortar method is drawn, showing that weighted collocation is able to achieve almost the same accuracy as the integration-based mortar formulation.

In this paper, a new approach is proposed to improve efficiency of the integration procedure for mortar integrals within finite element mortar methods for contact. Appropriate approaches subdivide polygonal integration segments into triangular integration cells where well-established quadrature rules can be applied for numerical integration. Here, a subdivision of segments into quadrilateral integration cells is proposed and investigated in detail. By this procedure, the numerical effort is decreased because the number of integration cells is smaller and less quadrature points are needed. In all the aforementioned methods, necessary projections of integration points result in rational polynomials in the integrand. Thus, an exact numerical integration is impossible. Using quadrilateral integration cells additionally involves non-constant Jacobian determinants which further increases the polynomial degree of the integrand. Numerical experiments indicate, that the resulting increase in the error is small enough to be acceptable in consideration of the gained speed-up.

Two novel hierarchic finite element formulations for geometrically nonlinear shell analysis including the effects of transverse shear are presented. Both methods combine a fully nonlinear Kirchhoff-Love shell model with hierarchically added linearized transverse shear components. Thus, large rotations can be taken into account while circumventing the peculiar task of finding a corresponding parametrization of the rotation tensor. The two formulations differ in the way the transverse shear effects are included, either using hierarchic rotations or hierarchic displacements. The underlying assertion is that in most practical applications the transverse shear angles are small even for large deformations. This is confirmed by various numerical experiments. The hierarchic construction results in an additive strain decomposition into parts resulting from membrane and bending deformation and additional contributions from transverse shear. It requires at least C1-continuous shape functions, which can be easily established within the isogeometric context using spline based finite elements. As reported earlier, this concept is intrinsically free from transverse shear locking. In the nonlinear case it dramatically facilitates representation of large rotations in shell analysis.

In this contribution, variationally consistent inertia templates for B-spline and NURBS-based finite elements are proposed as a unified concept for two different purposes: Customization of the template allows construction of masses and reciprocal masses with desired properties like higher-order accuracy or improved dispersion behavior; Inertia scaling allows substantial speed-up for explicit dynamics by increased critical time steps.

The derivation of the template is based on a three-field parametrized functional as in previous works of the authors’ group, but with modified primary variables, namely displacement, velocity and mass-specific linear momentum. The latter allows for mass-preservation for non-constant density throughout the domain and is therefore an enhancement to the formulation proposed in Tkachuk and Bischoff (2015).

With the focus on B-spline and NURBS-based finite elements, the proposed template provides alternatives to the row-sum- lumped mass matrix, which is only 2nd order accurate independent of the polynomial order. Earlier proposed algebraically constructed higher order masses from the literature can be reconstructed in the variational setting described here as special instances. Furthermore, higher-order reciprocal masses can be constructed from the template. They are especially attractive for explicit dynamics as there is no extra expense per time step compared with lumped mass for linear problems. For non-linear problems only small overhead is expected, but this paper focuses on linear problems only and mainly undistorted meshes. Tuning the method towards inertia scaling, a reduction of the maximum eigenfrequency by 25%–40% is obtained in the examples herein, whereas the accuracy is higher than for lumped or consistent mass.

This work deals with computer simulations of contact problems using the finite element method. Two modifications are proposed for the mortar method, which is the method applied to discretise the contact. The first modification concerns the numerical calculation of so-called contact integrals. For the corresponding integration in general cases polynomial integrands have to be integrated over polygonal areas. In order to use ordinary numerical quadratures the polygonal areas are usually subdivided into triangular integration cells. In this work an alternative subdivision into quadrilateral integration cells is suggested, which yields less integrations points. With the numerical experiments described in this work it is shown that due to this reduction the numerical effort is decreased considerably without deteriorating the accuracy of integration significantly. The second modification improves the contact stresses of the dual mortar method. This method uses dual functions to approximate the Lagrange multiplier field, yielding the advantage that the dual mortar method is more efficient than the standard mortar method. However, the contact stresses of the dual mortar method are less accurate than the contact stresses of the standard mortar method. In this work a modification of the contact stresses based on an L2 projection is presented for the dual mortar method. Numerical experiments show that with the introduced L2 projection the accuracy of the contact stress of the dual mortar method is improved and comparable to the accuracy of the standard mortar method.

The stability and reflection-transmission properties of the bipenalty method are studied in application to explicit finite element analysis of one-dimensional contact-impact problems. It is known that the standard penalty method, where an additional stiffness term corresponding to contact boundary conditions is applied, attacks the stability limit of finite element model. Generally, the critical time step size rapidly decreases with increasing penalty stiffness. Recent comprehensive studies have shown that the so-called bipenalty technique, using mass penalty together with standard stiffness penalty, preserves the critical time step size associated to contact-free bodies. In this paper, the influence of the penalty ratio (ratio of stiffness and mass penalty parameters) on stability and reflection-transmission properties in one-dimensional contact-impact problems using the same material and mesh size for both domains is studied. The paper closes with numerical examples, which demonstrate the stability and reflection-transmission behavior of the bipenalty method in one-dimensional contact-impact and wave propagation problems of homogeneous materials.