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In Part I, eigenvalues and eigenmodes of typical plane element stiffness matrices were separated and traced. This has important implications for the viability of new elements (presence of zero energy modes) and integrability of dynamic equations (critical time steps). In this part of the paper, similar techniques are applied to well‐known solid element stiffness matrices, and to some new ones.

The eigenvalues of element stiffness matrices K and the eigenvalues of the generalized problem Kx = λMx, where M is the element's mass matrix, are of fundamental importance in finite element analysis. For instance, they may indicate the presence of ‘zero energy modes’, or control the critical timestep applicable in temporal integration of dynamic problems. Recently explicit formulae for the eigenvalues of the stiffness matrix of a plane, 4‐node rectangular element have been given, and the authors have extended this approach to deal with 8‐node solid brick elements as well. In the present paper, explicit eigenvalues are given for plane triangular elements and techniques for eigenmode visualization are applied to well‐known triangular and quadrilateral elements. In the companion paper (Part II), the stiffness matrices of solid tetrahedra and bricks are similarly treated.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The detrimental effects of increased workloads and high-stakes accountability that impact on teachers’ job satisfaction and wellbeing have been well documented in the international literature (Holloway et al., 2017; Perryman et al., 2011). This chapter will explore the factors which influence staff mental health and wellbeing in schools. The authors unpack issues of burnout, job satisfaction and teacher attrition. The authors consider the concept of teacher resilience by situating resilience within a socio-ecological framework. Specifically, the authors draw on Greenfield’s (2015) model of teacher resilience. The authors draw on our own research to explore the relationship between staff wellbeing and student wellbeing (Glazzard & Rose, 2020). In addition, the authors consider the specific issues related to the wellbeing of school leaders.

Building on the introduction to positive psychology and positive education in Chapter 1, the aim of Chapter 3 is to focus on wellbeing and positive education in secondary schools. This includes an overview of approaches to intervening in mental health (‘traditional’ and those which draw on the principles of positive psychology) that have been used in schools, and the factors that can influence their outcomes. When and how to apply interventions across three levels: the system, the community, and the individual, are also explored, alongside four different approaches: whole school, whole class, small group, and one-to-one. The chapter draws on up-to-date research and practical experience in secondary school settings, and includes a case study of Positive Psychology in Practice, based on the delivery (by the author) of a multi-component PPI (mPPI) – The Hummingbird Project, which has now been delivered to approximately 4,000 students in 24 secondary schools across the North West of England. The effectiveness of the mPPI, key lessons learned and insights gained are shared, including how to overcome the challenges of working in a culture not conducive to positive education.

Mental health issues are exceedingly prevalent in society. Approximately one in five people will experience a mental illness within their lifetime and serious mental illnesses are most likely to emerge between the ages of 16 and 24. This research endeavored to gain a better understanding of teachers’ knowledge and perceived roles in dealing with students with mental health issues. The purpose of this paper is to explore teacher education programs and other resources accessible to teachers as well as barriers to their continued learning about issues related to mental health.

In total, 75 secondary school teachers completed an online survey consisting of 42 Likert-style questions constructed with the main objective of the study in mind. The questions were organized under five different subheadings in the survey in order to provide some direction regarding the research questions. Measures of central tendency were utilized to determine frequencies of responses. The researchers created summary tables of the data for analysis purposes.

Teachers indicate that it is within their role to deal with mental health issues, but many do not have the knowledge to do so. Teacher education programs are not providing enough preparation for teachers and, although available, many teachers do not have knowledge of resources produced by interest groups.

Teacher education programs, both pre-service and in-sevice, must respond to the needs of teachers. In doing so, the authors can then address the needs of students and assist them in the challenges that mental illnesses present.

While an educator's role does not officially include being a mental health practitioner, it is their role to educate all students. This inevitably requires an understanding of the connection between mental health issues and how they affect a student's ability to learn and to live a healthy life.

Resiliency theory suggests “the most important and consistent protective factor is that of adults caring for children during or after major stressors” (Masten et al., 1991, p. 431). Who better placed to assist them than teachers?

This research adds to the ever-increasingly difficulty tasks that teachers are charged with implementing. It identifies a clear need for increased attention to preparing teachers.

The use of algebraic languages such as REDUCE makes possible the automatic generation, from fairly concise data, of the main families of two and three dimensional C0 continuous finite element shape functions, with a high confidence in their correctness. This paper gives a tutorial introduction to the REDUCE language and describes how it was used to generate shape function routines.

A system for doing finite element computations in parallel is described. It is general purpose in the sense that it can be used across a wide range of finite element applications and in the sense that it is not restricted to any particular parallel hardware. Its performance on computers ranging from clusters of PCs to massively parallel high performance machines is illustrated.

The study was based around the following three research questions: What factors affect teacher well-being and mental health? How does teacher well-being and mental health impact on the progress of students? What resilience strategies are used by highly effective teachers with poor mental health to ensure that their students thrive? The paper aims to discuss this issue.

The research study was qualitative in nature and involved ten primary schools in England. Teachers and head teachers were interviewed. Each school visit also included a pupil discussion group with children from Years 3. In total, the research team interviewed 35 education professionals and 64 pupils.

Teachers reported a number of work-related stress triggers including busy times of the year, such as assessment periods, the pressure of extra curricula activities, the unexpected, keeping up with the pace of change and changes in school leadership. Children were attuned to their teacher’s mood and could usually pick up when they were feeling stressed, even if teachers tried to hide it.

No studies have used pupil voice to explore pupil perspectives of the impact of teacher mental health on their learning and progress. This is the first study of its kind.

Teachers are often the first contact for students with mental health difficulties. They are in an ideal position to identify students who are struggling and frequently support them using different approaches and techniques. The purpose of this paper is to investigate secondary school teachers’ experiences of supporting the mental health of their students.

Seven secondary school teachers from state-funded schools in the UK participated in face-to-face semi-structured interviews. Interpretative phenomenological analysis was used to understand and structure the data into themes.

Five superordinate themes emerged from the data analysis: perceived role of teacher, nature of relationship, barriers to helping the child, amount of training and resource, and helplessness and satisfaction. Participants described the lack of training, resource and clarity about their role to be causes of frustration. Internal and environmental factors often influenced participants’ feelings of helplessness.

The findings from this study cannot be readily generalised to the wider population due to the nature of qualitative interviews.

This study has led to a greater understanding of the experiences of teachers within a school setting. It is crucial that mental health training for teachers directly meets their needs and abilities.

This paper finds value in recognising the lived experience and difficulties faced by teachers supporting students’ mental health problems. A theoretical model is presented based on this analysis that can help inform best practice for schools.