Serving the Numerical Simulation community since 1989 
Meshless methods, also known as mesh-free methods, are computational techniques used for the approximation of the solutions of partial differential equations in the engineering and applied sciences. The advertised advantage of the method is that users do not have to worry about meshing. However, eliminating the meshing problem has introduced other, more complex issues. Oftentimes, advocates of meshless methods fail to mention their numerous disadvantages.
The World-Wide Failure Exercise (WWFE) was an international research project with the goal of assessing the predictive performance of competing failure models for composite materials. Part I (WWFE-I) focused on failure in fiber-reinforced polymer composites under two-dimensional (2D) stresses and ran from 1996 until 2004. Part II was concerned with failure criteria under both 2D and 3D stresses, and ran between 2007 and 2013. Part III, also launched in 2007, was concerned with damage development in multi-directional composite laminates.
Engineering students first learn statics, then strength of materials, and progress to the theories of plates and shells, continuum mechanics, and so on. As the course material advances from simple to complex, students often think that each theory (model) stands on its own, overlooking the fact that simpler models are special cases of the more complex ones. This view guided the development of the finite element (FE) method in the 1960s and 70s, and ultimately led to legacy FE codes adopting an “element-centric” approach.
Model development projects are essentially scientific research projects. As such, they are subject to the operation of the Kuhn Cycle, named after Thomas Kuhn, who identified five stages in scientific research projects: Normal Science, Model Drift, Model Crisis, Model Revolution, and Paradigm Change. The Kuhn cycle is a valuable concept for understanding how mathematical models evolve. It highlights the importance of paradigms in shaping model development and the role of paradigm shifts in the process.
From the beginning of FEM acceptance, a significant communication gap existed between the engineering and mathematical communities. Engineers did not understand why mathematicians would worry so much about the number of square-integrable derivatives, and mathematicians did not understand how it is possible that engineers can find useful solutions even when the rules of variational calculus are violated (variational crimes). This gap widened over the years: On one hand, the art of finite element modeling became an integral part of engineering practice. On the other hand, the science of finite element analysis became an established branch of applied mathematics.
At present, a very substantial unrealized potential exists in numerical simulation. Simulation technology has matured to the point where management can realistically expect the reliability of predictions based on numerical simulations to match the reliability of observations in physical experimentation. This will require management to upgrade simulation practices through exercising simulation governance.
Digital transformation is a multifaceted concept with plenty of room for interpretation. Its common theme emphasizes the proactive adoption of digital technologies to reshape business practices with the goal of gaining a competitive edge. The scope, timeline, and resource allocation of digital transformation projects depend on the specific goals and objectives. Here, we address digital transformation in the engineering sciences, focusing on numerical simulation.
The idea of a digital twin originated at NASA in the 1960s as a “living model” of the Apollo program. When Apollo 13 experienced an oxygen tank explosion, NASA utilized multiple simulators and extended a physical model of the spacecraft to include digital simulations, creating a digital twin. This twin was used to analyze the events leading up to the accident and investigate ideas for a solution. The term “digital twin” was coined by NASA engineer John Vickers much later. While the term is commonly associated with modeling physical objects, it is also employed to represent organizational processes. Here, we consider digital twins of physical entities only.
Models, developed under the discipline of VVUQ, can be relied on to make correct predictions within their domains of calibration. However, model development projects lacking the discipline of VVUQ tend to produce wrong models.
Certification by Analysis (CbA) uses validated computer simulations to demonstrate compliance with regulations, replacing some traditional physical tests. CbA allows for exploring a wide range of design scenarios, accelerates innovation, lowers expenses, and upholds rigorous safety standards. The key to CbA is reliability. This means that the data generated by numerical simulation should be as trustworthy as if they were generated by carefully conducted physical experiments. To achieve that goal, it is necessary to control two fundamentally different types of error; the model form error and the numerical approximation error, and use the models within their domains of calibration.
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