Analytic and numerical solutions in the theory of elastic plates

ABSTRACT

Numerical approximations of the solution of a boundary value problem when an exact solution is not available can be constructed by means of a variety of methods. In this paper, we present a technique that is based on the integral representation of the solution of an elliptic problem and the properties of the associated layer potentials. The procedure is illustrated in application to the mathematical model of bending of plates with transverse shear deformation in a finite domain, in the presence of Dirichlet, Neumann, and Robin conditions prescribed on the boundary.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

Back to the future: A retrospective assessment of model‐based scenarios for the management of the shrimp fishery in French Guiana facing global change

While the number of models dedicated to predicting the consequences of alternative resource management strategies has increased, instances in which authors look back at past predictions to learn from discrepancies between these and observed developments are scarce. In the past decades, the French Guiana shrimp fishery has experienced shrimp market globalization and decreasing levels of shrimp recruitment due to environmental changes. In 2006, a bio‐economic model of this fishery was developed to simulate its possible responses to economic and environmental scenarios up to 2016. Here, we compare here these predictions to the observed trajectories. While the number of active vessels corresponds to that which was predicted, the estimated shrimp stock does not. Important driving factors had not been anticipated, including a general strike, natural disasters, and the end of the global financial crisis. These results show the importance of participative approaches involving stakeholders in the co‐construction and shared representation of scenarios. Recommendations for resource managers

• Effective fisheries resources management and a fortiori, the capacity of the fisheries to adapt to global change, requires understanding of both ecological and economics dynamics.
• The temporal trajectory of the trawling shrimp fisheries has been well monitored, and the decline of both stock and fleet is understood regarding ecological and economic changes: Changes in the environmental conditions of shrimp recruitment, and oil price increase and selling price decrease.
• However, our bio‐economic modeling work showed that, even with a good understanding of the dynamics explaining past trajectories, unpredictable events (strike, natural disasters…) have acted as other key driving factors altering the capacity of the model to represent possible futures.
• These results led us to recommend a better integration of the expertise of social and political scientists in developing models of bio‐economic systems to increase the quality of scenario predictions, and to argue for more participative approaches involving the stakeholders.

     

Phase-field approach to fracture for finite-deformation contact problems

The present contribution deals with a variationally consistent Mortar contact algorithm applied to a phase-field fracture approach for finite deformations, see [4]. A phase-field approach to fracture allows for the numerical simulation of complex fracture patterns for three dimensional problems, extended recently to finite deformations (see [2] for more details). In a nutshell, the phase-field approach relies on a regularization of the sharp (fracture-) interface. In order to improve the accuracy, a fourth-order Cahn-Hilliard phase-field equation is considered, requiring global C¹ continuity (see [1]), which will be dealt with using an isogeometrical analysis (IGA) framework. Additionally, a newly developed hierarchical refinement scheme is applied to resolve for local physical phenomena e.g. the contact zone (see [3] for more details). The Mortar method is a modern and very accurate numerical method to implement contact boundaries. This approach can be extended in a straightforward manner to transient phase-field fracture problems. The performance of the proposed methods will be examined in a representative numerical example. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

DEM-FEM coupled numerical investigation of granular materials to increase crashworthiness of double-hull vessels

In this contribution, a novel design strategy is investigated for improving the crashworthiness of double-hull vessels, which involves usage of granular materials. For numerical simulation, a framework based on coupling of the Discrete Element and the Finite Element Method is used to study load bearing capacity of granular materials during uniaxial compression. In addition, the effect of Young's modulus of particles is also investigated with respect to the load transferability. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Minimization- and Saddle-Point-Based Modeling of Diffusion-Deformation-Processes in Hydrogels

Hydrogels have gained importance during the last years due to their wide range of synthetically fabricable elastic properties as well their increasing meaning in biomedical applications. Future exploitation of the vast prospects of hydrogels is however only feasible by establishing reliable material models that precisely capture their behavior in different environments. To this end, we propose a consistent variational framework for deformation-diffusion processes, offering a canonically compact approach to the chemo-mechanical coupling of hydrogels via a saddle-point as well as a new minimization formulation. The work depicts the construction of rate-type potentials for the chemo-mechanical evolution problem and their transformation into time-discrete incremental potentials. In terms of spatial discretization, the finite element method is employed, benefiting from the intrinsic symmetric structure of the variational foundation. While the saddle-point formulation yields the well-known LBB condition as a constraint for finite element interpolations, on the part of its minimizing counterpart H(Div, ℬ︁)-conforming elements have to be chosen. We illustrate appropriate solutions to both challenges, using mixed Taylor-Hood for the saddle-point and Raviart-Thomas elements for the minimization formulation and discuss advantages of the new approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Unexpected Formation of a 2,2′-Di( N -ethyl-acetamino)substituted Diphenyl Disulfane on Oxidation of 3-Ethyl-2-methylbenzothiazolium Tetrafluoroborate

Attempts at the oxidation of 3-ethyl-2-methylbenzothiazolium salt 2 with a variety of oxidizing reagents did not lead to the desired isochiral S -oxide 3 or achiral S , S -dioxide 4 , in some cases, however, unexpectedly to the ring-opened dimeric 2,2'-di( N -ethyl-acetamino)substituted diphenyl disulfane 5 , the molecular structure of which was confirmed by x-ray analysis. The synthesis of 2-methylbenzothiazole- S , S -dioxide 14 , reported by Zincke et al. in 1915, turned out to be not reproducible. \centerline{\epsfbox{:art:fig-01.jpg}}