**Introduction**

The finite method of analysis has been widely used for solid works analyses and simulation. The method works around displacement of the component material. The method (FEM), or finite element examination (FEA), is built on the idea of constructing a complicated object with simple blocks, or, dividing a complicated object into small and manageable pieces (Bathe, 2008). Application of this simple idea can be found everywhere in everyday life as well as in engineering.

The finite element analysis was developed in 1943 for the Courant or the variational methods (Cook, 2007). Later on, in 1956, the system was developed further for stiffness analysis while in 1960 it was designed to solve problems that mainly involve planar structures (dhatt, Lafrana, & touzot, 2012).The years around 1970 saw the system applied to mainframe computers while the 1980s the system was developed for microcomputers and finally 1990s saw the application of the system for large structural analysis (Reddy, 1993). However, the finite method has been widely applied by NASA because of the humongous amounts of money required in the design of rockets and other aerospace technology (Hughes, 2012). The method cuts down the costs required because of the number of prototypes that need to be designed. Therefore, the analysis is based on the ability to successfully design and implement technology and reduces the number of attempts that may lead to failure (Cyprien, 2017)

For structural analysis, the first step is to break down the structure into smaller components and later on a description of the properties such as Young’s modulus and the stiffness among others (Akin, 2010). The third step is the connection of the individual elements at the nodes whereby equations will be formed. Finally, equations are formed for the eventuality of the quantities that are to be determined. Some of the properties to be determined by this last step include stresses, displacement, and strain.

**Shortcoming of finite element analysis and remodeling.**

The evolution in the field of engineering has led to the design of various models to be used in the finite element analysis. Though they are numerous, they have been founded on the basic principles of ordinary differential equations and partial differential equation (hughes, 2012). Furthermore, the traditional forms of finite element analysis have had numerous shortcomings such as in the analysis of fluids and wave analysis (Rhughes, 2012). By observing these shortcomings, the model has been revisited and can be applied on various fronts.

**Load cell**

Load cells have been used extensively for on-field analysis of complex structures (Hoe, 2012). It is not easy to calculate the number and quantity of loads that a structure can sustain and as such, many models have been designed and used (Maranzano & Hancook, 2016). The working principle of load cells lies on the sensing capability. These instruments can sense torque and force and as reliable as can be when properly used and designed.

The most widely used load cell is the strain gauge (Muller, de Brito, & Perreira, 2010). Basically, these devices are designed in such a way that they are able to hold the material to be tested. The strain gauge has been described as a foil that is composed of many components but the primary element used for sensing the load and force is a thin foil resistor (Olmi, 2015). However, this load cell changes according to the load and can deform to every unique load it encounters (Muller, de brito, & Perreira, 2010).

The short duration of time that the load may be subjected to a load cell is enough for the analysis. The functioning of these load cells is based on n numerical analysis whereby transient force may be calculated using the Kelvin-Voight element of analysis (Maranzano & Hancook, 2016). The element of analysis focuses on qualitative impact as well as resonance and nonlinear behavior. The impact load is converted to an electric signal and some may be based on piezoelectric materials. It is a matter of concern because load cells that utilize piezoelectric materials to generate electric signal have been used in numerous research in the analysis of dynamic varying forces

**Linear static analyses**

Figure 1: Basic geometry of load cell. |

**Analysis Methodology using solid works**

The solid works analysis tool present the user with an array of options on the analysis methodology to be used. Basically, there are three options presented to the user and depend on the type of solid work analysis to be involved: the part, the assembly and the drawing options. In this analysis, the focus will be on the part option.

Depending on the units to be used in the design, the user may select any of the four options presented. However, the units to be used in this analysis are abbreviated by MMGS (millimeter, gram, second)

The second step is to ensure that the working plane is as per the user’s orientation. As per our drawing, the sketch is provided on the front plane and as such, the front plane is sketched with the dimensions provided.

The front plane

Sketched diagram

The frame is provided in two dimensions and in order to extract a 3D model, the extrude option is selected. The diagram of the extruded model is as below.

The force is exerted on threaded holes and in order to do this on, a circle of 9mm radius is provided at the top and the cut-extrude option is selected to ensure that the circle runs through the three panels.

The strain lines are obtained by drawing lines as in the sketches above and extended throughout the whole width by using the split line option.

In our analysis, the strain gauges are located 13mm from the half circle and 42 mm from the left face of the cell.The line is drawn 13mm from the half circle and is later on projected onto the face using the split line option.The same is repeated on the other side resulting into the following.

This is followed by indicating the various locations at which the sensors are to be located. It is from these sensor locations that the strain values will be obtained. The steps to insert the sensors is shown by the following menu diagrams:

Location of sensor menu

Selection of sensor locations

With all the above in place, the material properties are input by selecting carbon steel which, as per the recommendations has the required properties. The properties are indicated below:

The next step is to provide the loading conditions and as per the 375 load, the basic procedure is as follows. Select fixtures, follow this by fixed geometry and then the split faces to select the faces that the loading is to occur.

The external load pop out menu provides the user with the type of load to be applied including torque, force, temperature load etc.

In this, we select ‘force’ then proceed to select the faces on which the load will be applied.

There is an option that provides the user with the choice of face and the resulting diagram will be as follows:

All this in place, the next step is to ensure that the meshing options as per the finite element analysis are input. Basically, we go to the meshing option and from the popup menu, select the mesh size. In our analysis, the mesh size was 4mm and the resulting mesh is as depicted.

All the above are preliminary input and in trying to determine the robustness and stresses around the model, we run the program. Running the program provides the user with different views of the stress, strain and displacement.

As per our above model, the stress and displacement is as follows:

Stress

The maximum stress is 2.15e*7 while the minimum is 42.34N/m2

Displacement

The maximum displacement is 0.037 while the minimum is 0.00

**Strain**

The maximum strain is 7.10886e-005 while the minimum strain is 2.563e-010

An intermediate model in the analysis

The final aspect in the analysis is to find strain and stress at specified sensor. The y can be found by following the following procedure:

Select strain from the result submenu then select probe.

Strain

The same procedure is used to find the stress values and are as follows:

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Stresses

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**Hand calculations**

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Software calculations are actually based on the stiffness matrix and the separation of the different elements into panels. The beginning and end of each panel is defined by nodes and as per the requirements, the global or local coordinate system is used in the analysis.

Element | Length | Sine | cosine |

1 | 164 | 0 | 1 |

2 | 164 | 0 | 1 |

3 | 82 | 0 | 1 |

4 | 82 | 0 | 1 |

This is the stiffness matrix for the individual elementsr.Furthermore,c represents the sine while cs represents the cosine. The area is denoted by A while the length denoted by l

The stiffness matrix for element 1=K= the calculation is based on the global coordinate system whereby the movement is limited in the x and y directions only. The same applies to the other elements because of the indifference in angle

3 4 5 6

K= the second matrix covers the first node

5 6 7 8

K= the third matrix covers the third node

7 8 9 10

K= the final matrix covers the final node

The third step is to ensure that the matrix coefficients are uniform throughout. The assumption made in the calculation is that all the elements have uniform area throughout and therefore can be easily eliminated from the equation

The general matrix may be obtained by multiplying the coefficient of the last 2 nodes by 2.

K=

K=

Therefore, the final matrix for the whole structure may be put as:

Solving the matrix we get the displacement at the point of loading which is 1.46e-9 meters

The stresses that will be inflicted on that specific point may be estimated from the equation: which is

The above equation is applied to each node specified by the user.

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**Conclusion**

Based on the software, the analysis indicates that there is need for structural support for the plate to be robust and stable. This is due to the force acting on it at the upper end. Furthermore, the analysis provides a regional distribution of the various displacements and stresses induced by 375N force.

The solid works software reduces the need for the numerous hand calculations and is based on the finite element analysis iterations to complete the stress and strain calculations (lombard, 2008). It may be considered to be among the best software because of the detailed analysis d and the detailed solutions provided (Kurowski, 2013). However, there are numerous software that may be used in the analysis but with different specifications.

# References

Akin, J. E. (2010). *Finite element analysis concepts via solidworks.*

Bathe, k. J. (2008). *finite eklement method.*

Cook, R. D. (2007). *Concepts and applications of finite element analysis.*

Cyprien. (2017). *What is linear static analysis in FEA simulation*. Retrieved 12 20, 2017, from fearforall.com/linear-ststic-analysis-fea/

dhatt, G., Lafrana, E., & touzot, E. (2012). *Finite element method.*

Hoe, Y. S. (2012). *finite element method.*

Hughes, T. J. (2012). *The finite element method:kinear,sytatic and dynamic finite element analysis.*

Kurowski, P. (2013). *Emgineering analysis with solidworks simulation 2013.*

lombard, M. (2008). *Solidworks 2007 bible.*

Maranzano, B. J., & Hancook, B. C. (2016). sensing and bio sensing research. *7*.

Muller, I., de brito, R. M., & Perreira, C. E. (2010). load cells in force sensing analysis-theory and a novel application. *13*(1).

Olmi, G. (2015). *load cell training for students.*

Rhughes, T. J. (2012). *The finite element method:linear static analysis and dynamic finite element analysis.*