To obtain accurate and reliable results of finite element analysis (FEA) requires a high level of expertise and the full-scale physical context information, which are bottlenecks restricting the application of achievements of FEA in industry. This paper proposes an ontology-based framework including a hierarchy transfer approach and a three-stage automated finite element analysis method to solve these problems. The hierarchy transfer approach is proposed to create different transfer formats according to the data, information, and knowledge, to carry out the integration at different levels. The knowledge found in design and FEA theories is presented by ontology in order to uniformly describe the physical phenomenon with the same semantic meanings. This involves the development of a shared design and FEA ontology, as well as, specific application ontologies in the Ontology Web Language (OWL). The three-stage automated finite element analysis method is applied to mark up artifact in problem definition, to reuse domain knowledge in problem formulation, and to enable the automation of the FEM analysis process in the solution routine with the application of AI techniques. The feasibility and effectiveness of the framework and concepts are empirically validated by a case study.