It could be shown that the shape function matrix for this tetrahedron element is of the...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
It could be shown that the shape function matrix for this tetrahedron element is of the following form of a (12x3) matrix: N₁ 0 0 0 0 N3 0 0 N₁ 00N3 0 N₁0 N₂ 0 and the S matrix for a three-dimensional finite element is: N = B = b₁ 0 0 0 0 N₂ N₂ N₁ 0 0 N₂ 0 0 д/ду 0 0 a/əz 0 д/дz д/ду д/дх 0 a/az a/ay a/ax 0 Given that B = SN, write down, in terms of N, (i=1,2,3,4) and the partial differential operators (i.e. a/ax, a/ay and a/az), the mathematical form of the matrix elements b₁, C₁, d3 and d4 in the following B matrix: 0 0 b₂ 0 0 C1 0 \d₁ S = /a/ax 0 C1 0 d₁ 0 b₁ 0 C2 d₁ C₁ 0 0b₁d₂ 0 C2 0 d₂ 0 0 C3 0 0 0 0 N₁ 0 N3 0 0 N₁ 0 b3 0 0 0 C3 0 b₂ d₂ C₂ 0 b₂ d3 0 0 0 0 0 b4 0 0 0 0 0 C4 d3 0 0 b3 0 C4 b4 d3 C3 0 d4 0 b3 d4 0 d4 0 C4 b4 It could be shown that the shape function matrix for this tetrahedron element is of the following form of a (12x3) matrix: N₁ 0 0 0 0 N3 0 0 N₁ 00N3 0 N₁0 N₂ 0 and the S matrix for a three-dimensional finite element is: N = B = b₁ 0 0 0 0 N₂ N₂ N₁ 0 0 N₂ 0 0 д/ду 0 0 a/əz 0 д/дz д/ду д/дх 0 a/az a/ay a/ax 0 Given that B = SN, write down, in terms of N, (i=1,2,3,4) and the partial differential operators (i.e. a/ax, a/ay and a/az), the mathematical form of the matrix elements b₁, C₁, d3 and d4 in the following B matrix: 0 0 b₂ 0 0 C1 0 \d₁ S = /a/ax 0 C1 0 d₁ 0 b₁ 0 C2 d₁ C₁ 0 0b₁d₂ 0 C2 0 d₂ 0 0 C3 0 0 0 0 N₁ 0 N3 0 0 N₁ 0 b3 0 0 0 C3 0 b₂ d₂ C₂ 0 b₂ d3 0 0 0 0 0 b4 0 0 0 0 0 C4 d3 0 0 b3 0 C4 b4 d3 C3 0 d4 0 b3 d4 0 d4 0 C4 b4
Expert Answer:
Related Book For
Horngrens Accounting
ISBN: 978-0133855388
10th Canadian edition Volume 2
Authors: Tracie L. Miller-Nobles, Brenda L. Mattison, Ella Mae Matsumura, Carol A. Meissner, Jo-Ann L. Johnston, Peter R. Norwood
Posted Date:
Students also viewed these mathematics questions
-
This exercise tests your understanding of the four inventory methods. List the name of the inventory method that best fits the description. Assume that the cost of inventory is rising. 1....
-
This exercise tests your understanding of the four inventory methods. List the name of the inventory method that best fits the description. Assume that the cost of inventory is rising. 1. ----...
-
A. The Rilex and Chill Coffee Shop has requested a cash budget for August. After examining the records of the company, you find the following: 1. Cash balance on 1 August is RM43,280. 2. Actual sales...
-
L-keys, such as the one shown in the figure below, are commonly used to insert screws and bolts in medical implants. This insertion process can be simplified into the loading scenario shown in the...
-
An investigation into why emergency medical service (EMS) workers leave the profession was published in the Journal of Allied Health (Fall 2011). The researchers surveyed a sample of 244 former EMS...
-
The CFO for Yong Corporation is discussing with the companys CEO issues related to the companys short-term obligations. Presently, both the current ratio and the acid-test ratio for the company are...
-
With Figure 1.5 in mind, how could changes in government policies affect accounting activities? All Stakeholders Financial statements Bank & agency reports Accounting System Tax returns Management &...
-
1. What breaches of fiduciary duty does the Adelphia case raise? 2. Why do you think the Rigas Family thought they could get away with using Adelphia as their own piggy bank? 3. What allowed the...
-
The pressure of both tanks were 117.7 kpa.( first picture) We added 500kg mass to the left tank and the pressure went up to 118.7. (second picture) Can you explain why the pressure changed after...
-
During 2018, Mings Book Store paid $486,000 for land and built a store in Naperville, Illinois. Prior to construction, the city of Naperville charged Mings $1,000 for a building permit, which Mings...
-
1) showed the needed resources, activities conducted, and program outputs. 2) How The hierarchy of intended outcomes starting with initial, intermediate, and long-term changes in knowledge, skills,...
-
Required Question # 1 (40 marks, How has Pepsi Corporation performed over the 10-year time period from 1981 to 1990? In your critical discussion focus on qualitative and quantitative indicators....
-
From the following balances extracted from the books of Kiran and the additional information, prepare the trading and profit and loss account for the year ended 31st March, 2020 and also show the...
-
Building Accounts Receivable Prepaid Insurance Cash Equipment supplies Land Insurance Expense Depreciation Expense supplies Expense Ahmad, drawing Unearned Revenues $128,800 Ahmad, Capit 14,520...
-
Show the solution in good accounting form E10-5B: (Indicators of Liquidity and Leverage) Financial statements of CARROTS Corporation are reproduced below. The market price of Carrot's ordinary share...
-
At its January 15 meeting, the board of directors of Omega Consolidated Industries made a decision to build a new manufacturing facility in China and approved funding up to $180 million for...
-
What accounting software and tools do accountants commonly use to perform their duties? How does an accountant assist in tax planning and ensuring compliance with tax laws?
-
Match each of the key terms with the definition that best fits it. _______________ A record of the sequence of data entries and the date of those entries. Here are the key terms from the chapter. The...
-
Financial institutions such as insurance companies and pension plans hold large quantities of bond investments. Suppose Meridian Credit Union purchases $2,000,000 of 3.0 percent bonds of the Province...
-
Pacific Hotels Inc., a large hotel chain, had Retained Earnings of $250.0 million at the beginning of 2017. The company showed these figures at December 31, 2017: ($ millions) Net income $75.0 Cash...
-
Ace Properties Ltd. purchased a five-year, 4.5 percent Scotia bond on May 1, 2017, and intends to hold it until it matures. The market rate at the time was 5.2 percent. Interest is paid annually each...
-
1. Describe the bases of power held by Dr. Jamie Thompson. Describe the bases of power held by Dr. Elizabeth Clarke. 2. What activities and people have contributed to Jaime Thompsons power? What...
-
What is the current in the wire in Figure Q22.1? 1.0 VR + 1.0-1.0V + FIGURE Q22.1
-
Electroconvulsive therapy is a last-line treatment for certain mental disorders. In this treatment, an electric current is passed directly through the brain, inducing seizures. The total charge that...
Study smarter with the SolutionInn App