# Archives

### Uncertainities in Topology Optimization

Various types of uncertainties are considered in the topology optimization, like uncertainty in loading, geometry and material properties, etc. Two methods account for the uncertainties in the topology optimization framework. They are- 1. Probabilistic based methods (Statistical or reliability-based methods) 2. Non-probabilistic based methods The traditional approach to account for the uncertainties in the structure […]

### Extrude 2D geometry to 3D geometry in Comsol

Select 2D space dimension and select specific physics. Model some 2D geometry under Geometry 1 tab. Now, go to add component option under Home Tab and click on 3D. Right click on Geometry 2 and click on work plane. Work Plane 1 option now appears under Geometry 2 button and Plane Geometry option now appears […]

### Explicit Dynamic Analysis

Need for explicit dynamic analysis Implicit and explicit are the two main types of time integration methods that are used to perform dynamic simulations. The explicit time integration is more efficient for the following situations- 1. To simulate the buckling and complex contact problem. 2. To model material deformation and failure at a high strain […]

### Architected Materials: Metamaterials

Metamaterials are those materials that are not found in nature and are artificially manufactured materials. The properties of such materials are derived from their internal microstructure (geometrical configuration) and not from their chemical composition. The concept of metamaterials was initially coined in the context of optics and electromagnetism. The properties of the metamaterials on the […]

### Numerical Challenges occurs in SIMP based Topology Optimization

A) Checkerboard Pattern: a) Checkerboarding refers to the formation of alternate solid and void elements in the final topologically optimized structure and possesses artificial high stiffness to the numerical model. b) This issue is primarily due to the discretization error of the numerical FE model. c) It occurs mainly in those models which have been […]

### Mesh refinement in Topology Optimization

Mesh refinement or discretization is a fundamental step in finite element analysis. In finite element analysis, the refinement of mesh is done only in those areas that are of interest (eg: the region of high stress in the stress analysis) so that to obtain good accuracy with minimum computational efforts. However, in the context of […]

### Size, Shape and Topology Optimization

Structural optimization is determining the best possible material distribution within a physical volume domain to transmit the applied load safely. To achieve this, the constraints imposed by the manufacturer and eventual use must also be considered. These may include increasing stiffness (increasing strain energy or minimizing compliance), minimizing stress levels, minimizing displacement, altering the fundamental […]

### Nonlinearities in Structure

When the force-displacement relation of the system is linear, then that particular type of system is named as “linear system.” The simplest example of such a system is mass-spring mechanical assembly. In this mechanical system, the stiffness of a spring remains constant. But in real-world problems, the stiffness of a system is not linear; however, it may be idealized […]

### Norm and condition number of a matrix

In a numerical analysis with a vector involvement, norms are essential to predict the various errors involved in the numerical analysis. A norm is a function ||.|| in a vector space V. If A is a n*n matrix, then its norm is a real number and denoted by ||A||. A norm satisfies the following properties: […]

### Different Topology optimization solvers used in Ansys

In Ansys commercial FE package, two topology optimization solvers are present based on the SIMP (Solid isotropic material with penalization) method. These solvers include Optimality Criteria (OC) and Sequential Convex Programming (SCP). Sequential Convex Programming: This method is an extension of the Method of Moving Asymptotes (MMA) solver. The MMA solver is a non-linear programming-based […]