**is a mathematical approach that optimizes material layout within a given design space, for a given set of loads and boundary conditions such that the resulting layout meets a prescribed set of performance targets.**

*Topological Optimization*Why is this an valuable design process to arrive at a conceptual design proposal? And if it is valuable why has it not been implemented in the arena of architecture to a much higher degree?

Well it is a valuable design process and it has been implemented in architectural design through trial and error in the past but it has not been available as a method of informing design for the average architect until the advent of the computer and easy to use advanced software in the past decade.

Architects have taken a quantum leap towards recognizing the relationship of topological optimization and nature through simple studies of structural elements commonly used in traditional building methods. They have discovered through the use of advanced software programs that living structures found in nature are inherently optimized to make use of the least amount of material for "the given design space, set of loads, boundary conditions" and function.

The following research shows a simple architectural element : a cantilevered truss : and the use of Topological Optimization to minimize the use of material - in this case a large steel plate.

First we will define the Problem Statement & Design Criteria

The next step is to calculate to initial material weight and define the constraints of the design space. In this case we are using a set size (boundary) for the cantilevered structure and we will be using steel as our material to calculate the initial weight. We will also use an estimated maximum load in addition to the weight of the steel to find out optimized plate geometry.

Having set up the material layout and design space with the set loads I used the following procedures to implement a design through discoveries in Topological Optimization and verifying structural analysis models. This can take many forms using many different methods. In this case I used the following sequence of procedures to initialize,produce a design model and verify.

The first step in the analysis is to make sure the base case plate structure is feasible.

Now that we know the base case works so we can move on to Topological Optimization of the element. In this case we will be importing the geometry into Altair and will set up model and performance targets.

Next we set-up the model to verify displacement matches our initial model. If it does we know it is calculating the loads correctly and we can move on to the Topology Optimization stage.

The stresses match - the next step is to run the Topology Optimization of the cantilevered plate.

The final frame shows our optimized cantilevered truss. The next step is to import the geometry into the structural analysis software in order to verify the optimized geometry.

Lastly we can plug the new geometry into the design model to envision the aesthetic quality and present to the client for approval or further input.