. According to (Gomes , et al., 2013) the three main mathematical encounters with SIMP method are mesh dependency, checkboard patterns and local minima. To compensate for mesh-dependency and checkboard patterns instabilities, a well-known sensitivity filter brought forth by Bendose Sigmund is used (Gomes , et al., 2013). The local minima problem is dealt with by a continuation method with various increments in the function of the given filter (Gomes , et al., 2013). Pertaining to Bendose and Sigmund, the stiffness gained from SIMP model can be grasped as the stiffness of structures consisting of void and a quantity of solid material for the given density of the structure’s material (Zhu, et al., 2016). Because of the simplicity of SIMP
*…show more content…*

The problems can be solved as void if ρ = 0 or associated material if ρ =1. Therefore, if ρ tends to be zero, the stiffness in that given element is zero, which means the element can be deleted because it is no longer important for the structure (Rao, et al., n.d.). However, if the density reaches one then that element is of dire importance to the structure and cannot be deleted (Rao, et al., n.d.). If this simple formulation is used, the total elastic energy measure (U) can be used as the objective function of the optimisation problem. This formulation is written below: Minimise: U n=1.....,N Subject to: ∑_(N-1)^N▒〖〖ρ〗_n V_n=V_0 〗 (2.1) 0 ≤ ρn ≤ 1 n = 1……,N This formulation in equation (1) and can also be extended to suite multiple load case problems by minimising the weight of the total elastic energies. The following equation expresses formulation for a multi-load case topology problem, using a weighted sum function for multi-load cases. Minimise: ∑_(j=1)^j▒〖w_j U_j 〗 Subject to: ∑_(N-1)^N▒〖ρ_n V_n=V_0 〗 (2.2) 0 ≤ ρn ≤ 1 n = 1,….,N Solving a Topology problem using this energy based minimum compliance topology optimisation

Related

- Decent Essays
## Beam Project

- 1345 Words
- 6 Pages

The goal of the beam project is to design and construct a beam that can hold a given amount of weight without breaking. The beam is required to hold a concentrated load of 375 lbf on the X-axis and 150 lbf on the Y-axis. The maximum allowable weight of the beam is 250 grams. The maximum allowable deflection for the beam is 0.230 in. and 0.200 in. for the X and Y-axis respectively. The beam is required to be 24 in. in length, and it will be tested on a simply supported configuration spanning 21 in. All calculations are to be done under the assumption that the density of basswood is 28 lbm/ft3 and the modulus of elasticity for basswood is 1.46x106 lbm/in2. Given the constraints of a spending cost of $10.50, a maximum beam weight of 250 grams,

- 1345 Words
- 6 Pages

Decent Essays - Decent Essays
## Aerospace Engineering Personal Statement

- 1292 Words
- 6 Pages

With modern computational methods, most notably finite element analysis, designers are now able to simulate the response of a structure under a multitude of highly complex loading conditions. Another important aspect of these tools are their ability to solve ever increasingly complex problems in a faster time than ever before. These advanced computational tools also allow engineers to optimize designs much faster. These new optimal designs will improve the strength and stiffness of structures and lower their weight. This will not only improve a design's performance, but also help improve efficiency. These abilities are very exciting since they allow for a more fully developed and accurate picture of a structure's performance evident even in the most demanding

- 1292 Words
- 6 Pages

Decent Essays - Decent Essays
## Analysis Of The 15-33 Method By Shannon Kirk

- 1316 Words
- 6 Pages

The 15/33 Method by Shannon Kirk is an amazing emotional roller coaster that follows the life of a sixteen year old rich, pregnant, genius. Although she is not named throughout the entire book, the reader gets a great insight on her peculiar character. Every detail about her is shared in the book from the age of six. Unusual things have always occurred in her life, but when she was kidnapped after school, even she was taken off guard. Each detail from her past creates an understanding for the reader of how she was able to kill her captor in cold blood. Throughout her captivity she created a foolproof plan, she collected different assets to help her execute her plan, and after a full thirty three days into captivity she carried her plan

- 1316 Words
- 6 Pages

Decent Essays - Decent Essays
## Quain Case Analysis Essay examples

- 1005 Words
- 5 Pages

The first shows the impact of changing the objective function coefficients on the optimal solution and gives the range of values (lower and upper bound) for which the optimal solution remains unchanged. The second part of the report shows the impact of changing the R.H.S of the constraints of the objective function value, with the help of Dual Value (Shadow Price), with the lower and upper bounds for which the shadow price is valid. The results of this analysis in POM are as follows:

- 1005 Words
- 5 Pages

Decent Essays - Decent Essays
## Math Exploration Task

- 1169 Words
- 5 Pages

They are simple yet effective mathematical tools, with many different applications in science and engineering. The equations of equilibrium will enable us to calculate the reactions and internal member forces in a truss.

- 1169 Words
- 5 Pages

Decent Essays - Better Essays
## Bending of Open Channel Section Report Essays

- 2017 Words
- 9 Pages

Experiment Two: Stiffness Report from laboratory work performed on 12 May 2011 as a part of the unit of study CIVL2201 Structural Mechanics

- 2017 Words
- 9 Pages

Better Essays - Decent Essays
## Ap Physics Lab

- 1594 Words
- 7 Pages

\parindent{\ \ \ }Figure~\ref{fig:mdg} shows the average strain at different time instants for various mesh densities. The variation in the results obtained with the finest mesh and the mesh immediately next to the finest one is less than 5\%. Hence, we can reasonably assume that the study reached convergence. The difference in results obtained from the dense mesh (i.e., mesh 6) and coarse mesh (i.e., mesh 3) is less than 8\%.

- 1594 Words
- 7 Pages

Decent Essays - Good Essays
Engineering involves a wide array of problems that must be overcome. A great deal of time is spent researching materials and their properties. Materials compromise all aspects of our society, from buildings to roads to even the equipment that was used in this lab. Problems arise in regards to how strong or flexible the material is, with the official terms being stress, strain, and elasticity. Improper use of such materials results in tragedies such as the Tacoma Narrows Bridge in Washington that failed to due resonance and stress beyond its elastic limit [1].

- 1155 Words
- 5 Pages

Good Essays - Satisfactory Essays
## Novum Case Summary

- 84 Words
- 1 Pages

Novum’s six distinctive lightweight structural products were developed to inventively solve demanding architectural challenges. The systems are typically fabricated in our high quality factories, architecturally finished and shipped compactly. The products share the basic principal of being mechanically fastened on site, hence achieving the precision required for direct cladding and often avoiding the need for secondary structure.

- 84 Words
- 1 Pages

Satisfactory Essays - Decent Essays
## Truss Design

- 563 Words
- 3 Pages

His theory maintains that the truss is a structure that represents beam behaviour. Generally, Culmann considers every connection of the members in a truss flexible (basically a hinge) and formulates equilibrium equations at the point where members meet (Culmann 1851). Nowadays, this theory is known as the "Method of Joints" and is regularly used to calculate the internal forces in each member of the truss. Armed with a method to calculate the forces in the members of a truss, engineers optimized the design of trusses through addition and variation of

- 563 Words
- 3 Pages

Decent Essays - Good Essays
## Tibia Essay

- 1196 Words
- 5 Pages

After the model was imported into Abaqus, the mechanical properties earned from the prior process were assigned to the model. In addition, as the model is assumed as a homogenous structure, then the highest values of all mechanical properties were used as a representative of all structure. These properties are density of 1813 kg/m3, young modulus of 4993 MPa and Poisson coefficient of 0.3 (see figure 4).

- 1196 Words
- 5 Pages

Good Essays - Satisfactory Essays
## What Are Trusses?

- 365 Words
- 2 Pages

A Structure that is consisting of members or elements which work only in tension or compression is called truss. The trusses are designed with triangular or pyramidal shape, where members are assembled so the system works as one. Assembled members usually are triangle shaped, they are connected to each other with gusset joints that are: riveted, bolted or welded. The truss is a two-force member, that is a structural component where force is applied only in two points. Maine structures in what trusses usually used are bridges, platforms, towers, roofs and floor structures.

- 365 Words
- 2 Pages

Satisfactory Essays - Decent Essays
## Strength Of Trusses Essay

- 1177 Words
- 5 Pages

The experiment we chose to accomplish was to test trusses and observe which upheld the most weight. Obvious constraints were placed on this, as it was not just open-ended. All trusses were to be based off the same design, with just the addition of more vertical beams on various trusses, the number of beams incrementing steadily.

- 1177 Words
- 5 Pages

Decent Essays - Decent Essays
## The Cooper-JACOB Time-Jacob Method

- 1344 Words
- 6 Pages

Since the test was done in a well in the Karoo Supergroup, it should be noted that the Theis method tent to measure errors during the drawdown observed during the constant rate test, specifically when the drawdown is measured manually (van Tonder et al., 2001a).

- 1344 Words
- 6 Pages

Decent Essays - Decent Essays
## Strength of Materials 4th Ed. by Ferdinand L. Singer

- 17787 Words
- 72 Pages

Simple stresses are expressed as the ratio of the applied force divided by the resisting area or σ = Force / Area. It is the expression of force per unit area to structural members that are subjected to external forces and/or induced forces. Stress is the lead to accurately describe and predict the elastic deformation of a body. Simple stress can be classified as normal stress, shear stress, and bearing stress. Normal stress develops when a force is applied perpendicular to the cross-sectional area of the material. If the force is going to pull the material, the stress is said to be tensile stress and compressive stress develops when the material is being compressed by two opposing forces. Shear stress is developed if the

- 17787 Words
- 72 Pages

Decent Essays