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Using examples of flexible mechanisms, demonstrates that while the Newmark method is unstable for nonlinear dynamics, time step refinement could in some cases lead to even earlier onset of instability in the form of a blown‐up response. As a remedy, develops a plane finite beam element based on the Simo‐Vu Quoc formulation for dynamics and integrates it with an energy‐conserving midpoint time‐stepping rule for solving problems in nonlinear dynamics. Shows that this combination produces a consistently stable and accurate dynamic analysis method even for large time steps.

The purpose of this paper is to examine quadratic convergence of finite element analysis for hyperelastic material at finite strains via Abaqus‐UMAT as well as classification of the rates of convergence for iterative solutions in regular cases.

Different formulations for stiffness – Hessian form of the free energy functionals – are systematically given for getting the rate‐independent analytical tangent and the numerical tangent as well as rate‐dependent tangents using the objective Jaumann rate of Kirchoff stress tensor as used in Abaqus. The convergence rates for available element types in Abaqus are computed and compared for simple but significant nonlinear elastic problems, such as using the 8‐node linear brick (B‐bar) element – also with hybrid pressure formulation and with incompatible modes – further the 20‐node quadratic brick element with corresponding modifications as well as the 6‐node linear triangular prism element and 4‐node linear tetrahedral element with modifications.

By using the Jaumann rate of Kirchoff stress tensor for both, rate dependent and rate independent problems, quadratic or nearly quadratic convergence is achieved for most of the used elements using Abaqus‐UMAT interface. But in case of using rate independent analytical tangent for rate independent problems, even convergence at all is not assured for all elements and the considered problems.

First time the convergence properties of 3D finite elements available in Abaqus sre systematically treated for elastic material at finite strain via Abaqus‐UMAT.

The objective of this work is to develop an element technology to recover the plane stress response without any plane stress specific modifications in the large strain regime. Therefore, the essential feature of the proposed element formulation is an interface to arbitrary three‐dimensional constitutive laws. The easily implemented and computational cheap four‐noded element is characterized by coarse mesh accuracy and the satisfaction of the plane stress constraint in a weak sense. A number of example problems involving arbitrary small and large strain constitutive models demonstrate the excellent performance of the concept pursued in this work.

First, a synopsis of the major changes of natural science, mathematics and philosophy within the 17th century shall highlight the birth of the new age of science and technology. Based on Fermat's principle of the shortest light‐way and Galilei's first attempt of an approximative solution of the so‐called Brachistochrone problem using a quarter of the circle, Johann Bernoulli published a competition for this problem in 1696, and six solutions were submitted by the most famous scientists of the time and published in 1697, even though the variational calculus was only published in 1744 by Euler for the first time. Especially the analytical solution of Jakob Bernoulli contains already the main idea of Euler's variational calculus, i.e. to vary only one function value at a time using a finite difference method and proceeding to the infinitesimal limit. Also Leibniz' geometric solution is very remarkable, realizing a direct discrete variational method geometrically which was invented numerically much later in the 19th century by Ritz and Galerkin and generalized to the finite element method by introducing test and trial functions in finite subspaces. A new finite element solution of the non‐linear Brachistochrone problem concludes the paper. It is important to recognize that besides the roots of variational calculus also the first formulations of conservation laws in mechanics and their applications originated in the 17th century.

This chapter discusses the evolution of German views on public debt 1850–1920, referring to three strands of secondary literature: (1) German retrospectives on public finance, (2) the historical literature with a public choice perspective, and (3) contributions to public/constitutional law, mainly referring to Lorenz von Stein. The skeptic view of public debt endorsed by authors of the second half of the period is shown to be related to politico-economic issues of state agency combined with new state functions, rather than to the rejection of Dietzel’s Proto-Keynesian macroeconomic reasoning.

Nobody concerned with political economy can neglect the history of economic doctrines. Structural changes in the economy and society influence economic thinking and, conversely, innovative thought structures and attitudes have almost always forced economic institutions and modes of behaviour to adjust. We learn from the history of economic doctrines how a particular theory emerged and whether, and in which environment, it could take root. We can see how a school evolves out of a common methodological perception and similar techniques of analysis, and how it has to establish itself. The interaction between unresolved problems on the one hand, and the search for better solutions or explanations on the other, leads to a change in paradigma and to the formation of new lines of reasoning. As long as the real world is subject to progress and change scientific search for explanation must out of necessity continue.

Due to the emergence of rich personal narratives within recent research, the purpose of this paper is to review and to explore the experience of transition from care and consider how these accounts can inform care services.

This meta-synthesis follows from several quantitative and mixed method reviews examining how young people experience aging out of the care system.

Three themes emerged from an inductive analysis: navigation and resilience – an interrelated process; the psychological impact of survival; and complex relationship.

The findings of a meta-synthesis should not be over generalised and are at least partially influenced by the author's epistemological assumptions (Dixon-Woods et al., 2006). However, a synthesis of this topic has the potential to provide greater insight into how transition can be experienced through the reconceptualising of the personal experiences across the studies reviewed (Erwin et al., 2011).

This synthesis discusses the themes; their relationship to existing research and policies, and suggestions for further exploration. The experience of transition is considered critically in terms of its often traumatic nature for the young person aging out of care but also the ways in which the experience itself can build essential resiliencies.

Reflections for clinical practice are discussed with importance placed upon systemic working, accommodating likely challenges and considering appropriate therapeutic approaches for the client group and their systems.

No review thus far has qualitatively examined the narratives told by the young people emerging from care and how these narratives have been interpreted by the researchers who sought them (Hyde and Kammerer, 2009).

The proliferation of social networking sites (SNSs) has drawn attention to different parties in realising their goals. Advertisers utilise SNSs to promote new products and services; politics optimise SNSs to gather support from the public, while ordinary users use SNSs as a unique platform to practice self-disclosure, develop networks, and sustain relationships. This study explores how social anxiety affects self-disclosure on SNSs and well-being. It also examines the moderating effects of two contextual factors, namely, online disinhibition and psychological stress. Two hundred and thirty-four valid responses were collected via an online survey. A positive relationship between social anxiety and self-disclosure, and self-disclosure and well-being was found. Furthermore, a positive moderation effect among social anxiety, online disinhibition, and self-disclosure was revealed. This research contributes to the development of social networking literature. It also enhances the understanding of disclosure patterns on SNSs among socially anxious individuals, thereby providing important insights for practitioners, educators, and clinicians.

Special education in the USA is, in most respects, a 20th century phenomenon and is now governed primarily by federal legislation first enacted in 1975. The federal law in its most recent reauthorization (2004) continues to require a free appropriate public education (FAPE) for all students with disabilities, a full continuum of alternative placements (CAP) ranging from residential or hospital care to inclusion in general education, an individual education plan or program (IEP) for each student identified as needing special education, and placement in the least restrictive environment (LRE) that is thought best for implementing the IEP. Parents must be involved in the special education process. Approximately 14 percent of public school students were identified for special education in 2004–2005, but the number and percentage of students identified in most high-incidence categories as needing special education have declined in recent years (the total for all categories was about 8.5 percent of public school students in 2010). A variety of evidence-based interventions can be used to address the wide range of instructional and behavioral needs of students with disabilities and their families, including transition to further education or work, family services, and teacher education. Special education in the USA may find new sources of support and thrive or may become less common or be abandoned entirely due to criticism and withdrawal of support for social welfare programs of government.