Johannes Altenbach

Bio: Johannes Altenbach is an academic researcher from Otto-von-Guericke University Magdeburg. The author has contributed to research in topics: Creep & Finite element method. The author has an hindex of 8, co-authored 21 publications receiving 626 citations.

On generalized Cosserat-type theories of plates and shells: a short review and bibliography

Abstract: One of the research direction of Horst Lippmann during his whole scientific career was devoted to the possibilities to explain complex material behavior by generalized continua models. A representative of such models is the Cosserat continuum. The basic idea of this model is the independence of translations and rotations (and by analogy, the independence of forces and moments). With the help of this model some additional effects in solid and fluid mechanics can be explained in a more satisfying manner. They are established in experiments, but not presented by the classical equations. In this paper the Cosserat-type theories of plates and shells are debated as a special application of the Cosserat theory.

Closed and approximate analytical solutions for rectangular Mindlin plates

Abstract: Basing on the Nadai-Levy and the Vlasov-Kantorovich methods closed and approximate analytical solutions of Mindlin's plate equations in the case of rectangular plates are discussed. For elastic, homogeneous and isotropic plates three unknowns of the governing two-dimensional boundary value problem are formulated as series of products of functions depending on a single coordinate. Specifying the functions for one of the in-plane coordinate directions the governing partial differential equations for a special type of boundary conditions and the principle of virtual displacements for the general case yield a set of ordinary differential equations. The analytical solution of these equations provides expressions for functions depending on the other in-plane coordinate. For plates with simply supported edges for one of the coordinate directions and for arbitrary homogeneous boundary conditions for the other one the Nadai-Levy method provides a closed or exact solution in the sense that the infinite series for displacements and stress resultants can be truncated to obtain any desired accuracy. In the general case of nonsimply supported edges the iterative Vlasov-Kantorovich method yields an approximate analytical solution. Both methods are nonsensitive to a reduction of the thickness with respect to accuracy and represent the boundary layer solutions in terms of exponential functions. Applications to rectangular plates with various types of boundary conditions are presented.

On the Prediction of Creep Damage by Bending of Thin-Walled Structures

Abstract: Analysis of thin-walled structures operating at elevated temperaturesneeds a consideration of time-dependent creep-damage behaviour. Within theframework of the creep theory and the CDM the irreversible deformations ofthe structural elements can be described by constitutive equations withinternal state variables. The paper deals with an application ofphysically based creep-damage constitutive model with two damageparameters, proposed by Hayhurst, to the stress analysis of thin-walledplates and shallow shells. The governing equations of the shell theory areformulated by the consideration of geometrical nonlinearities associatedwith time-dependent finite deflections. Numerical examples show aninfluence of the finite deflections on the life-time predictions in platesas well as illustrate a dependence of damage evolution on the stress statemode. The results for creep damage evolution in plates are compared withresults based on the classical Kachanov–Rabotnov creep-damageconstitutive model.

Fiber-Reinforced Polymer Composites: Manufacturing, Properties, and Applications.

Abstract: Composites have been found to be the most promising and discerning material available in this century. Presently, composites reinforced with fibers of synthetic or natural materials are gaining more importance as demands for lightweight materials with high strength for specific applications are growing in the market. Fiber-reinforced polymer composite offers not only high strength to weight ratio, but also reveals exceptional properties such as high durability; stiffness; damping property; flexural strength; and resistance to corrosion, wear, impact, and fire. These wide ranges of diverse features have led composite materials to find applications in mechanical, construction, aerospace, automobile, biomedical, marine, and many other manufacturing industries. Performance of composite materials predominantly depends on their constituent elements and manufacturing techniques, therefore, functional properties of various fibers available worldwide, their classifications, and the manufacturing techniques used to fabricate the composite materials need to be studied in order to figure out the optimized characteristic of the material for the desired application. An overview of a diverse range of fibers, their properties, functionality, classification, and various fiber composite manufacturing techniques is presented to discover the optimized fiber-reinforced composite material for significant applications. Their exceptional performance in the numerous fields of applications have made fiber-reinforced composite materials a promising alternative over solitary metals or alloys.

A non-classical Mindlin plate model based on a modified couple stress theory

Abstract: A non-classical Mindlin plate model is developed using a modified couple stress theory. The equations of motion and boundary conditions are obtained simultaneously through a variational formulation based on Hamilton’s principle. The new model contains a material length scale parameter and can capture the size effect, unlike the classical Mindlin plate theory. In addition, the current model considers both stretching and bending of the plate, which differs from the classical Mindlin plate model. It is shown that the newly developed Mindlin plate model recovers the non-classical Timoshenko beam model based on the modified couple stress theory as a special case. Also, the current non-classical plate model reduces to the Mindlin plate model based on classical elasticity when the material length scale parameter is set to be zero. To illustrate the new Mindlin plate model, analytical solutions for the static bending and free vibration problems of a simply supported plate are obtained by directly applying the general forms of the governing equations and boundary conditions of the model. The numerical results show that the deflection and rotations predicted by the new model are smaller than those predicted by the classical Mindlin plate model, while the natural frequency of the plate predicted by the former is higher than that by the latter. It is further seen that the differences between the two sets of predicted values are significantly large when the plate thickness is small, but they are diminishing with increasing plate thickness.

Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models

Abstract: Hencky (Uber die angenaherte Losung von Stabilitatsproblemen im Raum mittels der elastischen Gelenkkette. Ph.D. thesis, Engelmann, 1921) proposed a discrete model for elasticae by introducing rigid bars and rotational springs. Hencky (Proc R Soc Lond A Math Phys Eng Sci 472(2185), 2016) approach has been introduced to heuristically motivate the need of second gradient continua. Here, we present a novel numerical code implementing directly the discrete Hencky-type model which is robust enough to solve the problem of the determination of equilibrium configurations in the large deformation and displacement regimes. We apply this model to study some potentially applicable problems, and we compare its performances with those of the second gradient continuum model. The numerical evidence presented supports the conjecture that Hencky-type converges to second gradient model.

Advances in pantographic structures: design, manufacturing, models, experiments and image analyses

Abstract: In the last decade, the exotic properties of pantographic metamaterials have been investigated and different mathematical models (both discrete or continuous) have been introduced. In a previous publication, a large part of the already existing literature about pantographic metamaterials has been presented. In this paper, we give some details about the next generation of research in this field. We present an organic scheme of the whole process of design, fabrication, experiments, models and image analyses.