TOPOLOGY OPTIMIZATION OF STRUCTURES & VALUE ENGINEERING

Topology Optimization of Structures & Value Engineering

Value Engineering in construction is a process or methodology that works to minimize cost without compromising quality and functionality. In construction, the best time to initiate value analysis is the planning and design stage for maximum financial gain. Based on the teamwork approach, the methodology leads to benefits like cost, quality, sustainability, etc.

 

The construction industry continuously strives for optimum structures and values such as  safety, economy, and sustainability as the key structural design virtues. Topology optimization as a part of structural optimization helps predict a structure’s layout for an enhanced design. It helps bring a lighter and stiffer shape to the structure with a variety of feasible and sustainable design options preventing undue wastage and minimizing cost. By factoring constraints and performance at an early design stage speed up finalizing the design, saving a lot of effort and time.

What Is Topology Optimization

 

Structural topology is the internal spatial arrangement of the structure members, its joints, and boundaries. Topology optimization is the methodology of changing the spatial arrangement, joints, or boundaries of discrete or continuum structures.

Topology optimization works under different constraints of a structure (stress, displacement, buckling instability, and natural frequency) and constant parameters (applied loads, material type, etc.). It helps to identify the best position and size of the parts. Also, to find the better design of a structure, the topology optimization process suggests the radical changes in the geometry.

Topology Optimization Techniques

The two most widely recognized and used topology optimization techniques are – Evolutionary Structural Optimization (ESO) and Solid Isotropic Material with Penalization (SIMP). They use the Factor Element Method (FEM) for the discretization of the design domain into the finite element.

ESO Technique

ESO technique based on the concept of rejection performs the stepwise removal of inefficient parts from the initial structure and drive the structure towards an optimized configuration. For the rejection process, a predefined value of the rejection ratio gets referred. The technique lacks defining a rule for determining the control parameters like rejection ratios, evolution ratios, and tolerance parameters. Later, an Extended Evolutionary Technique got proposed with the concept of rejection and extension. The initial ESO method was lacking the extension concept. It included the idea of contour lines and bi-directional evolution.

SIMP Technique

SIMP technique develops an optimum structural shape by varying the material density under the designable domain. This designable domain gets usually defined by the Factor Element, used to analyze the structure. The basic approach followed by the SIMP technique for topology optimization is as follows:

Minimum Compliance DesignMinimum compliance design involves minimizing a particular performance measure (stress, displacement, buckling load, etc.) subjected to a constraint on the available resources.

Minimum Weight DesignIt minimizes the mass of the structure with constraints on the particular performance measure.

Topology Optimization in Architecture and Structural Engineering

 

During the 20th century, in architecture and structural engineering, several innovative methods were used to develop optimized structures. Those techniques resulted in the form of structurally and functionally efficient design with attractive architecture.

However, all these techniques came with a common limitation. The number of holes within the structure to be specified before the structural formation exercise. It required a physical analog model. Topology optimization overcame this limitation by effectively optimizing the number of holes or openings and creating an optimum structure from a block of material, as suggested by the designer.

Listed below are some of the exemplary applications of topology optimization in architecture and structural engineering:

Case study 1 – Unconventional Office Building Structure in Japan

As part of a Topology Optimization experiment, an office building was designed in Japan, making it structurally sound with pleasing aesthetics. The optimal number of holes, their location and shapes in the exterior reinforced wall were derived with topology optimization. The unique commercial building had the walls shaped in rectangular plates and optimized for vertical and horizontal load conditions.

Case study 2 – Doha Education Center’s Roof Canopy Structure

Doha Education center’s roof canopy structure is an example of the use of topology optimization purely for architectural purposes. The roof is shaped like a tree trunk and mimics the Sidra tree reflecting the grandeur of an architectural genius. A doubly-curved roof canopy supporting structure also got designed with topology optimization. Computer Numerical Controlled (CNC) milling technology created the formwork and built with reinforced concrete. In the case of large-scale projects, for implementing topology optimization, advanced manufacturing technology is also required.

 

Doha Education center’s roof canopy structure is an example of the use of topology optimization purely for architectural purposes. The roof is shaped like a tree trunk and mimics the Sidra tree reflecting the grandeur of an architectural genius. A doubly-curved roof canopy supporting structure also got designed with topology optimization. Computer Numerical Controlled (CNC) milling technology created the formwork and built with reinforced concrete. In the case of large-scale projects, for implementing topology optimization, advanced manufacturing technology is also required.

Steps of the Optimization Process

1. Define the Problem

The creation of an optimal structure through Topological optimization is mostly dependent on problem definition. A Problem statement for topology optimization consists of the following:

Objective Function – Each problem has a different objective, but most of them have a common objective to minimize the compliance or create a structure with maximum stiffness.

Main design variable Material distribution at each point member is the main design variable for almost all problems. Here, density gets represented in the form of 0 and 1. Where 1 represents material density and 0, where there is no material.

Design space It represents the volume for design. Several design factors, such as manufacturing and handling, helps to determine the design space. The value of design space remains unchanged even in the optimization stage.

Constraints The solution gets achieved after considering the structural constraints, as volume constraint (represents the amount of material to be distributed) and stress constraint.

2. Finite Element Analysis

The Finite Element Analysis (FEA) method evaluates design performance. A simple mesh of the design space is created and analyzed for stress distribution and strain energy. It helps in identifying the amount of load each section is handling.

3. Sensitivity Analysis

The sensitive analysis helps develop an element density plot considering the material constraints, design variables, and objective function within the design space. The element density plot guides where to place the high-density elements to attain the objective function. It shows the finite element density in the optimal solution, as inefficient sections get identified for trimming.

Sensitivity analysis is performed using topological optimization techniques based on material laws, like SIMP and BESO to obtain the optimum element density distribution plot.

4. Update Design Variable

After a few iterations, the trimming process gets performed to remove inefficient sections. Its impact on the overall structure is analyzed, and further, the design is updated.

The final design needs to meet the objective function defined with the obtained limited volume. In case the design achieved does not meet the objective, repeat the optimization process to get the desired result.

Benefits of Topology Optimization

Topology optimization helps in overcoming several challenges in the way to get an optimized structure. Some of the benefits offered by Topology optimization are:

Lighter and more efficient structure

Weight reduction is one of the best benefits of topology optimization. This optimization process helps in cutting down the excessive weight of a material without impacting its performance.

For example, GE used topology optimization to reduce 84 percent of the weight of its engine bracket.

The structural integrity of the material gets retained during weight reduction. Also, the shape gets streamlined to make it more efficient.

Cost-saving solutions

Topology optimization brings cost-saving solutions through its lightweight structure. Reduction in excessive weight, results in energy efficiency and other benefits, like lesser transportation cost that ultimately helps in cost savings.

GE’s weight reduction of the engine bracket benefited the airlines by saving almost 31 million dollars through energy efficiency.

Fast design process

Using topology optimization at the conceptual stage brings a design compatible with the design constraints and meets the expected performance. The time required to come up with the final structural design reduces and speeds up the construction process.

Sustainability

The undue material wastage gets reduced with the help of topologically optimized structures. The Energy efficiency of structures is also enhanced to bring a sustainable design with sound structural logic. Therefore, a sustainable structure gets created with the environment-friendly nature of topological optimization.

Optimum design based on different loads and conditions

Topological optimization helps to create complex structures. The designer analyzes several realistic loads’ scenarios at the initial design stage. It gives an advantage to the designer to try different geometry of elements. Therefore, the designer comes up with a stiff and aesthetically attractive structure. The structures with complex geometry also get constructed efficiently.

Expert Advice on Topology Optimization for Innovative and Sustainable Structures

Topology optimization at the conceptual stage is crucial for an innovative structural design and sustainable structure. Onestop AEC (OSA) is a reliable structural engineering service provider for years. Along with specialized services such as steel detailing, structural shop drawing, and rebar services, OSA’s expert advice and consultation can help you guide in the topology optimization process. Our customized structural optimization tools based on the project’s objective, material, and other constraints bring an optimum structure and value to the business. Contact us for a quick consultation today.

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