In simulation-based design, a key challenge is to formulate and solve analysis problems efficiently to evaluate a large variety of design alternatives. The solution of analysis problems has benefited from advancements in commercial off-the-shelf math solvers and computational capabilities. However, the formulation of analysis problems is often a costly and laborious process. Traditional simulation templates used for representing analysis problems are typically brittle with respect to variations in artifact topology and the idealization decisions taken by analysts. These templates often require manual updates and "re-wiring" of the analysis knowledge embodied in them. This makes the use of traditional simulation templates ineffective for multi-disciplinary design and optimization problems. Based on these issues, this dissertation defines a special class of problems known as variable topology multi-body (VTMB) problems that characterizes the types of variations seen in design-analysis interoperability. This research thus primarily answers the following question: How can we improve the effectiveness of the analysis problem formulation process for VTMB problems? The knowledge composition methodology (KCM) presented in this dissertation answers this question by addressing the following research gaps: (1) the lack of formalization of the knowledge used by analysts in formulating simulation templates, and (2) the inability to leverage this knowledge to define model composition methods for formulating simulation templates. KCM overcomes these gaps by providing: (1) formal representation of analysis knowledge as modular, reusable, analyst-intelligible building blocks, (2) graph transformation-based methods to automatically compose simulation templates from these building blocks based on analyst idealization decisions, and (3) meta-models for representing advanced simulation templates VTMB design models, analysis models, and the idealization relationships between them. Applications of the KCM to thermo-mechanical analysis of multi-stratum printed wiring boards and multi-component chip packages demonstrate its effectiveness handling VTMB and idealization variations with significantly enhanced formulation efficiency (from several hours in existing methods to few minutes). In addition to enhancing the effectiveness of analysis problem formulation, KCM is envisioned to provide a foundational approach to model formulation for generalized variable topology problems.