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The first chapter introduces the basic concept of continuum mechanical modeling based on the equilibrium, the kinematics and the constitutive equation, which may be combined to a system of partial differential equations. This general concept is illustrated for the one-dimensional bar. The final part of this chapter presents the weighted residual method. This formal approach allows to derive the classical approximation methods of applied mechanics. To do so, different formulations, i.e. the strong formulation, the inner product, the weak as well as the inverse formulation are introduced.

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Introduction

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  • 发表日期：

    2026年

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  • Andreas Öchsner

摘要

The first chapter introduces the basic concept of continuum mechanical modeling based on the equilibrium, the kinematics and the constitutive equation, which may be combined to a system of partial differential equations. This general concept is illustrated for the one-dimensional bar. The final part of this chapter presents the weighted residual method. This formal approach allows to derive the classical approximation methods of applied mechanics. To do so, different formulations, i.e. the strong formulation, the inner product, the weak as well as the inverse formulation are introduced.