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This book is the second edition of an introduction to modern computational mechanics based on the finite element method. It includes more details on the theory, more exercises, and more consistent notation; in addition, all pictures have been revised. Featuring more than 100 pages of new material, the new edition will help students succeed in mechanics courses by showing them how to apply the fundamental knowledge they gained in the first years of their engineering education to more advanced topics.
In order to deepen readers’ understanding of the equations and theories discussed, each chapter also includes supplementary problems. These problems start with fundamental knowledge questions on the theory presented in the respective chapter, followed by calculation problems. In total, over 80 such calculation problems are provided, along with brief solutions for each.
This book is especially designed to meet the needs of Australian students, reviewing the mathematics covered in their first two years at university. The 13-week course comprises three hours of lectures and two hours of tutorials per week.

The derivation and understanding of Partial Differential Equations relies heavily on the fundamental knowledge of the first years of scientific education, i.e., higher mathematics, physics, materials science, applied mechanics, design, and programming skills. Thus, it is a challenging topic for prospective engineers and scientists.
This volume provides a compact overview on the classical Partial Differential Equations of structural members in mechanics. It offers a formal way to uniformly describe these equations. All derivations follow a common approach: the three fundamental equations of continuum mechanics, i.e., the kinematics equation, the constitutive equation, and the equilibrium equation, are combined to construct the partial differential equations.

This book uses a novel concept to teach the finite element method, applying it to solid mechanics. This major conceptual shift takes away lengthy theoretical derivations in the face-to-face interactions with students and focuses on the summary of key equations and concepts; and to practice these on well-chosen example problems.
For this new, 2nd edition, many examples and design modifications have been added, so that the learning-by-doing features of this book make it easier to understand the concepts and put them into practice.
The theoretical derivations are provided as additional reading and students must study and review the derivations in a self-study approach. The book provides the theoretical foundations to solve a comprehensive design project in tensile testing. A classical clip-on extensometer serves as the demonstrator on which to apply the provided concepts. The major goal is to derive the calibration curve based on different approaches, i.e., analytical mechanics and based on the finite element method, and to consider further design questions such as technical drawings, manufacturing, and cost assessment. Working with two concepts, i.e., analytical and computational mechanics strengthens the vertical integration of knowledge and allows the student to compare and understand the different concepts, as well as highlighting the essential need for benchmarking any numerical result.

Due to the good mechanical properties, flax fiber-reinforced epoxy composites
are being widely used as a green alternative to glass fiber composites. However,
plant fibers absorb moisture from the environment, being in a higher moisture
uptake as the relative humidity (RH) increases. This absorbed moisture deteriorates the mechanical properties of the composites. In this study, geometric
and displacement potential function (DPF) approaches are used to predict the
mechanical properties of flax fiber-reinforced epoxy composites under environmental conditions, in particular, different RH values. The tensile properties
that were measured experimentally strongly agreed with the analytical findings.
Almost similar results were found for the tensile strain those were measured
experimentally and the one predicted by the geometric function.
However, the predicted strain values were 38% and 42% less than the experimental ones for 0% and 95% RH conditioned composites, respectively, when
DPF was used. Good conformity between the experimental, analytical, and
DPF formulation for predicting mechanical properties ensures the practical
applicability of this study. The formulations established in this work could,
therefore, be utilized to analytically solve laminated composites under specific
boundary conditions in structural applications.

We consider the mixed initial-boundary value problem in the context of the
Moore-Gibson-Thompson theory of thermoelasticity for dipolar bodies. We consider the case of heat conduction with dissipation. Even if the elasticity tensors
are not supposed to be positively defined, we have proven both, the uniqueness
and the instability of the solution of the mixed problem. In the case that the mass
density and the thermal conductivity tensor are positive, we obtain the uniqueness
of the solution using some Lagrange type identities.

This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function). The authors prove several basic results in distribution theory and present ordinary differential equations and partial differential equations by providing generalized solutions. In addition, the book deals with Sobolev spaces, which presents aspects related to variation problems, such as the Stokes system, the elasticity system and the plate equation. The authors also include approximate formulations of variation problems, such as the Galerkin method or the finite element method.
The book is accessible to all scientists, and it is especially useful for those who use mathematics to solve engineering and physics problems. The authors have avoided concepts and results contained in other books in order to keep the book comprehensive. Furthermore, they do not present concrete simplified models and pay maximal attention to scientific rigor.